#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:36777216")
using namespace std;
template <class T>
inline T &RD(T &);
template <class T>
inline void OT(const T &);
inline long long RD() {
  long long x;
  return RD(x);
}
inline double &RF(double &);
inline double RF() {
  double x;
  return RF(x);
}
inline char *RS(char *s);
inline char &RC(char &c);
inline char RC();
inline char &RC(char &c) {
  scanf(" %c", &c);
  return c;
}
inline char RC() {
  char c;
  return RC(c);
}
template <class T>
inline T &RDD(T &);
inline long long RDD() {
  long long x;
  return RDD(x);
}
template <class T0, class T1>
inline T0 &RD(T0 &x0, T1 &x1) {
  RD(x0), RD(x1);
  return x0;
}
template <class T0, class T1, class T2>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2) {
  RD(x0), RD(x1), RD(x2);
  return x0;
}
template <class T0, class T1, class T2, class T3>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3) {
  RD(x0), RD(x1), RD(x2), RD(x3);
  return x0;
}
template <class T0, class T1, class T2, class T3, class T4>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4) {
  RD(x0), RD(x1), RD(x2), RD(x3), RD(x4);
  return x0;
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5) {
  RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5);
  return x0;
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6) {
  RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6);
  return x0;
}
template <class T0, class T1>
inline void OT(const T0 &x0, const T1 &x1) {
  OT(x0), OT(x1);
}
template <class T0, class T1, class T2>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2) {
  OT(x0), OT(x1), OT(x2);
}
template <class T0, class T1, class T2, class T3>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3) {
  OT(x0), OT(x1), OT(x2), OT(x3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3,
               const T4 &x4) {
  OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3,
               const T4 &x4, const T5 &x5) {
  OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3,
               const T4 &x4, const T5 &x5, const T6 &x6) {
  OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);
}
inline char &RC(char &a, char &b) {
  RC(a), RC(b);
  return a;
}
inline char &RC(char &a, char &b, char &c) {
  RC(a), RC(b), RC(c);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d) {
  RC(a), RC(b), RC(c), RC(d);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d, char &e) {
  RC(a), RC(b), RC(c), RC(d), RC(e);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d, char &e, char &f) {
  RC(a), RC(b), RC(c), RC(d), RC(e), RC(f);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d, char &e, char &f, char &g) {
  RC(a), RC(b), RC(c), RC(d), RC(e), RC(f), RC(g);
  return a;
}
inline double &RF(double &a, double &b) {
  RF(a), RF(b);
  return a;
}
inline double &RF(double &a, double &b, double &c) {
  RF(a), RF(b), RF(c);
  return a;
}
inline double &RF(double &a, double &b, double &c, double &d) {
  RF(a), RF(b), RF(c), RF(d);
  return a;
}
inline double &RF(double &a, double &b, double &c, double &d, double &e) {
  RF(a), RF(b), RF(c), RF(d), RF(e);
  return a;
}
inline double &RF(double &a, double &b, double &c, double &d, double &e,
                  double &f) {
  RF(a), RF(b), RF(c), RF(d), RF(e), RF(f);
  return a;
}
inline double &RF(double &a, double &b, double &c, double &d, double &e,
                  double &f, double &g) {
  RF(a), RF(b), RF(c), RF(d), RF(e), RF(f), RF(g);
  return a;
}
inline void RS(char *s1, char *s2) { RS(s1), RS(s2); }
inline void RS(char *s1, char *s2, char *s3) { RS(s1), RS(s2), RS(s3); }
template <class T0, class T1>
inline T0 &RDD(T0 &a, T1 &b) {
  RDD(a), RDD(b);
  return a;
}
template <class T0, class T1, class T2>
inline T1 &RDD(T0 &a, T1 &b, T2 &c) {
  RDD(a), RDD(b), RDD(c);
  return a;
}
template <class T>
inline void RST(T &A) {
  memset(A, 0, sizeof(A));
}
template <class T>
inline void FLC(T &A, int x) {
  memset(A, x, sizeof(A));
}
template <class T>
inline void CLR(T &A) {
  A.clear();
}
template <class T0, class T1>
inline void RST(T0 &A0, T1 &A1) {
  RST(A0), RST(A1);
}
template <class T0, class T1, class T2>
inline void RST(T0 &A0, T1 &A1, T2 &A2) {
  RST(A0), RST(A1), RST(A2);
}
template <class T0, class T1, class T2, class T3>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3) {
  RST(A0), RST(A1), RST(A2), RST(A3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4) {
  RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5) {
  RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6) {
  RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);
}
template <class T0, class T1>
inline void FLC(T0 &A0, T1 &A1, int x) {
  FLC(A0, x), FLC(A1, x);
}
template <class T0, class T1, class T2>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x);
}
template <class T0, class T1, class T2, class T3>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x),
      FLC(A6, x);
}
template <class T>
inline void CLR(priority_queue<T> &Q) {
  while (!Q.empty()) Q.pop();
}
template <class T>
inline void CLR(stack<T> &S) {
  while (!S.empty()) S.pop();
}
template <class T>
inline void CLR(queue<T> &Q) {
  while (!Q.empty()) Q.pop();
}
template <class T0, class T1>
inline void CLR(T0 &A0, T1 &A1) {
  CLR(A0), CLR(A1);
}
template <class T0, class T1, class T2>
inline void CLR(T0 &A0, T1 &A1, T2 &A2) {
  CLR(A0), CLR(A1), CLR(A2);
}
template <class T0, class T1, class T2, class T3>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);
}
template <class T>
inline void CLR(T &A, int n) {
  for (int i = 0; i < n; ++i) CLR(A[i]);
}
template <class T>
inline bool EPT(T &a) {
  return a.empty();
}
template <class T>
inline T &SRT(T &A) {
  sort(A.begin(), A.end());
  return A;
}
template <class T, class C>
inline T &SRT(T &A, C cmp) {
  sort(A.begin(), A.end(), cmp);
  return A;
}
template <class T>
inline T &RVS(T &A) {
  reverse(A.begin(), A.end());
  return A;
}
template <class T>
inline T &UNQQ(T &A) {
  A.resize(unique(A.begin(), A.end()) - A.begin());
  return A;
}
template <class T>
inline T &UNQ(T &A) {
  SRT(A);
  return UNQQ(A);
}
template <class T, class C>
inline T &UNQ(T &A, C cmp) {
  SRT(A, cmp);
  return UNQQ(A);
}
const int MOD = int(1e9) + 7;
const int INF = 0x3f3f3f3f;
const long long INFF = 0x3f3f3f3f3f3f3f3fLL;
const double EPS = 1e-9;
const double OO = 1e20;
const double PI = acos(-1.0);
const int dx[] = {-1, 1, 0, 0};
const int dy[] = {0, 0, 1, -1};
template <class T>
inline bool checkMin(T &a, const T b) {
  return b < a ? a = b, 1 : 0;
}
template <class T>
inline bool checkMax(T &a, const T b) {
  return a < b ? a = b, 1 : 0;
}
template <class T, class C>
inline bool checkUpd(T &a, const T b, C c) {
  return c(b, a) ? a = b, 1 : 0;
}
template <class T>
inline T min(T a, T b, T c) {
  return min(min(a, b), c);
}
template <class T>
inline T max(T a, T b, T c) {
  return max(max(a, b), c);
}
template <class T>
inline T min(T a, T b, T c, T d) {
  return min(min(a, b), min(c, d));
}
template <class T>
inline T max(T a, T b, T c, T d) {
  return max(max(a, b), max(c, d));
}
template <class T>
inline T min(T a, T b, T c, T d, T e) {
  return min(min(min(a, b), min(c, d)), e);
}
template <class T>
inline T max(T a, T b, T c, T d, T e) {
  return max(max(max(a, b), max(c, d)), e);
}
template <class T>
inline T sqr(T a) {
  return a * a;
}
template <class T>
inline T cub(T a) {
  return a * a * a;
}
template <class T>
inline T ceil(T x, T y) {
  return (x - 1) / y + 1;
}
template <class T>
T abs(T x) {
  return x > 0 ? x : -x;
}
inline int sgn(double x) { return x < -EPS ? -1 : x > EPS; }
inline int sgn(double x, double y) { return sgn(x - y); }
inline double cos(double a, double b, double c) {
  return (sqr(a) + sqr(b) - sqr(c)) / (2 * a * b);
}
inline double cot(double x) { return 1. / tan(x); };
inline double sec(double x) { return 1. / cos(x); };
inline double csc(double x) { return 1. / sin(x); };
namespace CG {
inline double dist2(double x, double y) { return sqr(x) + sqr(y); }
struct Po {
  double x, y;
  Po(double x = 0, double y = 0) : x(x), y(y) {}
  void in() { RF(x, y); }
  void out() { printf("(%.2f,%.2f)", x, y); }
  inline friend istream &operator>>(istream &i, Po &p) {
    return i >> p.x >> p.y;
  }
  inline friend ostream &operator<<(ostream &o, Po p) {
    return o << "(" << p.x << ", " << p.y << ")";
  }
  Po operator-() const { return Po(-x, -y); }
  Po &operator+=(const Po &p) {
    x += p.x, y += p.y;
    return *this;
  }
  Po &operator-=(const Po &p) {
    x -= p.x, y -= p.y;
    return *this;
  }
  Po &operator*=(double k) {
    x *= k, y *= k;
    return *this;
  }
  Po &operator/=(double k) {
    x /= k, y /= k;
    return *this;
  }
  Po &operator*=(const Po &p) { return *this = *this * p; }
  Po &operator/=(const Po &p) { return *this = *this / p; }
  Po operator+(const Po &p) const { return Po(x + p.x, y + p.y); }
  Po operator-(const Po &p) const { return Po(x - p.x, y - p.y); }
  Po operator*(double k) const { return Po(x * k, y * k); }
  Po operator/(double k) const { return Po(x / k, y / k); }
  Po operator*(const Po &p) const {
    return Po(x * p.x - y * p.y, y * p.x + x * p.y);
  }
  Po operator/(const Po &p) const {
    return Po(x * p.x + y * p.y, y * p.x - x * p.y) / p.len2();
  }
  bool operator==(const Po &p) const { return !sgn(x, p.x) && !sgn(y, p.y); };
  bool operator!=(const Po &p) const { return sgn(x, p.x) || sgn(y, p.y); }
  bool operator<(const Po &p) const {
    return sgn(x, p.x) < 0 || !sgn(x, p.x) && sgn(y, p.y) < 0;
  }
  bool operator<=(const Po &p) const {
    return sgn(x, p.x) < 0 || !sgn(x, p.x) && sgn(y, p.y) <= 0;
  }
  bool operator>(const Po &p) const { return !(*this <= p); }
  bool operator>=(const Po &p) const { return !(*this < p); }
  double len2() const { return dist2(x, y); }
  double len() const { return sqrt(len2()); }
  double arg() const { return atan2(y, x); }
  Po &_1() { return *this /= len(); }
  Po &conj() {
    y = -y;
    return *this;
  }
  Po &lt() {
    swap(x, y), x = -x;
    return *this;
  }
  Po &rt() {
    swap(x, y), y = -y;
    return *this;
  }
  Po &rot(double a, const Po &o = Po()) {
    *this -= o;
    *this *= Po(cos(a), sin(a));
    return *this += o;
  }
  inline int q() const { return (y > 0 || y == 0 && x >= 0) ? 0 : 1; }
};
inline double dot(double x1, double y1, double x2, double y2) {
  return x1 * x2 + y1 * y2;
}
inline double dot(const Po &a, const Po &b) { return dot(a.x, a.y, b.x, b.y); }
inline double dot(const Po &p0, const Po &p1, const Po &p2) {
  return dot(p1 - p0, p2 - p0);
}
inline double det(double x1, double y1, double x2, double y2) {
  return x1 * y2 - x2 * y1;
}
inline double det(const Po &a, const Po &b) { return det(a.x, a.y, b.x, b.y); }
inline double det(const Po &p0, const Po &p1, const Po &p2) {
  return det(p1 - p0, p2 - p0);
}
inline double ang(const Po &p0, const Po &p1) {
  return acos(dot(p0, p1) / p0.len() / p1.len());
}
inline double ang(const Po &p0, const Po &p1, const Po &p2) {
  return ang(p1 - p0, p2 - p0);
}
inline double ang(const Po &p0, const Po &p1, const Po &p2, const Po &p3) {
  return ang(p1 - p0, p3 - p2);
}
inline double dist2(const Po &a, const Po &b) {
  return dist2(a.x - b.x, a.y - b.y);
}
template <class T1, class T2>
inline int dett(const T1 &x, const T2 &y) {
  return sgn(det(x, y));
}
template <class T1, class T2, class T3>
inline int dett(const T1 &x, const T2 &y, const T3 &z) {
  return sgn(det(x, y, z));
}
template <class T1, class T2, class T3, class T4>
inline int dett(const T1 &x, const T2 &y, const T3 &z, const T4 &w) {
  return sgn(det(x, y, z, w));
}
template <class T1, class T2>
inline int dott(const T1 &x, const T2 &y) {
  return sgn(dot(x, y));
}
template <class T1, class T2, class T3>
inline int dott(const T1 &x, const T2 &y, const T3 &z) {
  return sgn(dot(x, y, z));
}
template <class T1, class T2, class T3, class T4>
inline int dott(const T1 &x, const T2 &y, const T3 &z, const T4 &w) {
  return sgn(dot(x, y, z, w));
}
template <class T1, class T2>
inline double arg(const T1 &x, const T2 &y) {
  double a = ang(x, y);
  return ~dett(x, y) ? a : 2 * PI - a;
}
template <class T1, class T2, class T3>
inline double arg(const T1 &x, const T2 &y, const T3 &z) {
  double a = ang(x, y, z);
  return ~dett(x, y, z) ? a : 2 * PI - a;
}
template <class T1, class T2, class T3, class T4>
inline double arg(const T1 &x, const T2 &y, const T3 &z, const T4 &w) {
  double a = ang(x, y, z, w);
  return ~dett(x, y, z, w) ? a : 2 * PI - a;
}
template <class T1, class T2>
inline double dist(const T1 &x, const T2 &y) {
  return sqrt(dist2(x, y));
}
template <class T1, class T2, class T3>
inline double dist(const T1 &x, const T2 &y, const T3 &z) {
  return sqrt(dist2(x, y, z));
}
inline Po _1(Po p) { return p._1(); }
inline Po conj(Po p) { return p.conj(); }
inline Po lt(Po p) { return p.lt(); }
inline Po rt(Po p) { return p.rt(); }
inline Po rot(Po p, double a, const Po &o = Po()) { return p.rot(a, o); }
inline Po operator*(double k, const Po &p) { return p * k; }
inline Po operator/(double k, const Po &p) { return conj(p) * k / p.len2(); }
struct Line {
  Po a, b;
  Line(const Po &a = Po(), const Po &b = Po()) : a(a), b(b) {}
  Line(double x0, double y0, double x1, double y1)
      : a(Po(x0, y0)), b(Po(x1, y1)) {}
  Line(const Line &l) : a(l.a), b(l.b) {}
  Line(double A, double B, double C) {
    C = -C;
    if (!::sgn(A))
      a = Po(0, C / B), b = Po(1, C / B);
    else if (!::sgn(B))
      a = Po(C / A, 0), b = Po(C / A, 1);
    else
      a = Po(0, C / B), b = Po(1, (C - A) / B);
  }
  void in() { a.in(), b.in(); }
  inline friend istream &operator>>(istream &i, Line &p) {
    return i >> p.a >> p.b;
  }
  inline friend ostream &operator<<(ostream &o, Line p) {
    return o << p.a << "-" << p.b;
  }
  Line operator+(const Po &x) const { return Line(a + x, b + x); }
  Line operator-(const Po &x) const { return Line(a - x, b - x); }
  Line operator*(double k) const { return Line(a * k, b * k); }
  Line operator/(double k) const { return Line(a / k, b / k); }
  Po operator*(const Line &) const;
  Po d() const { return b - a; }
  double len2() const { return d().len2(); }
  double len() const { return d().len(); }
  double arg() const { return d().arg(); }
  int sgn(const Po &p) const { return dett(a, b, p); }
  int sgn(const Line &) const;
  bool sameSgn(const Po &p1, const Po &p2) const { return sgn(p1) == sgn(p2); }
  void getEquation(double &K, double &B) const {
    K = ::sgn(a.x, b.x) ? (b.y - a.y) / (b.x - a.x) : OO;
    B = a.y - K * a.x;
  }
  void getEquation(double &A, double &B, double &C) const {
    A = a.y - b.y, B = b.x - a.x, C = det(a, b);
  }
  Line &push(double r) {
    Po v = d()._1().lt() * r;
    a += v, b += v;
    return *this;
  }
};
inline double dot(const Line &l1, const Line &l2) {
  return dot(l1.d(), l2.d());
}
inline double dot(const Line &l, const Po &p) { return dot(l.a, l.b, p); }
inline double dot(const Po &p, const Line &l) { return dot(p, l.a, l.b); }
inline double det(const Line &l1, const Line &l2) {
  return det(l1.d(), l2.d());
}
inline double det(const Line &l, const Po &p) { return det(l.a, l.b, p); }
inline double det(const Po &p, const Line &l) { return det(p, l.a, l.b); }
inline double ang(const Line &l0, const Line &l1) {
  return ang(l0.d(), l1.d());
}
inline double ang(const Line &l, const Po &p) { return ang(l.a, l.b, p); }
inline double ang(const Po &p, const Line &l) { return ang(p, l.a, l.b); }
inline int Line::sgn(const Line &l) const { return dett(*this, l); }
inline Po Line::operator*(const Line &l) const {
  return a + d() * det(a, l) / det(*this, l);
}
inline Po operator&(const Po &p, const Line &l) {
  return l * Line(p, p + l.d().lt());
}
inline Po operator%(const Po &p, const Line &l) { return p & l * 2 - p; }
inline Line push(Line l, double r) { return l.push(r); }
struct Seg : public Line {
  Seg(const Po &a = Po(), const Po &b = Po()) : Line(a, b) {}
  Seg(double x0, double y0, double x1, double y1) : Line(x0, y0, x1, y1) {}
  Seg(const Line &l) : Line(l) {}
  Seg(const Po &a, double alpha) : Line(a, alpha) {}
  Seg(double A, double B, double C) : Line(A, B, C) {}
  inline int sgn(const Po &p) const;
  inline int sgn(const Line &l) const;
  inline bool qrt(const Seg &l) const;
  inline int sgn(const Seg &l) const;
};
inline int Seg::sgn(const Po &p) const {
  if (dett(p, a, b)) return -1;
  if (a == p || b == p) return 0;
  return -dott(p, a, b);
}
inline int Seg::sgn(const Line &l) const { return sgn(*this * l); }
inline bool Seg::qrt(const Seg &l) const {
  return min(a.x, b.x) <= max(l.a.x, l.b.x) &&
         min(l.a.x, l.b.x) <= max(a.x, b.x) &&
         min(a.y, b.y) <= max(l.a.y, l.b.y) &&
         min(l.a.y, l.b.y) <= max(a.y, b.y);
}
inline int Seg::sgn(const Seg &l) const {
  if (!qrt(l)) return -1;
  int d1 = dett(a, b, l.a), d2 = dett(a, b, l.b), d3 = dett(l.a, l.b, a),
      d4 = dett(l.a, l.b, b);
  if ((d1 ^ d2) == -2 && (d3 ^ d4) == -2) return 1;
  return ((!d1 && dott(l.a - a, l.a - b) <= 0) ||
          (!d2 && dott(l.b - a, l.b - b) <= 0) ||
          (!d3 && dott(a - l.a, a - l.b) <= 0) ||
          (!d4 && dott(b - l.a, b - l.b) <= 0))
             ? 0
             : -1;
}
inline double dist2(const Line &l, const Po &p) {
  return sqr(fabs(det(l.d(), p - l.a))) / l.len2();
}
inline double dist2(const Line &l1, const Line &l2) {
  return dett(l1, l2) ? 0 : dist2(l1, l2.a);
}
inline double dist2(const Seg &l, const Po &p) {
  Po pa = p - l.a, pb = p - l.b;
  if (dott(l.d(), pa) <= 0) return pa.len2();
  if (dott(l.d(), pb) >= 0) return pb.len2();
  return dist2(Line(l), p);
}
inline double dist2(const Seg &s, const Line &l) {
  Po v1 = s.a - l.a, v2 = s.b - l.a;
  double d1 = det(l.d(), v1), d2 = det(l.d(), v2);
  return sgn(d1) != sgn(d2) ? 0 : sqr(min(fabs(d1), fabs(d2))) / l.len2();
}
inline double dist2(const Seg &l1, const Seg &l2) {
  if (~l1.sgn(l2))
    return 0;
  else
    return min(dist2(l2, l1.a), dist2(l2, l1.b), dist2(l1, l2.a),
               dist2(l1, l2.b));
}
template <class T1, class T2>
inline double dist2(const T1 &a, const T2 &b) {
  return dist2(b, a);
}
}  // namespace CG
using namespace CG;
template <class T>
inline T &RD(T &x) {
  char c;
  while (!isdigit((c = getchar())))
    ;
  x = c - '0';
  while (isdigit((c = getchar()))) x = x * 10 + c - '0';
  return x;
}
template <class T>
inline T &RDD(T &x) {
  char c;
  while ((c = getchar()), c != '-' && !isdigit(c))
    ;
  if (c == '-') {
    x = '0' - (c = getchar());
    while (isdigit((c = getchar()))) x = x * 10 + '0' - c;
  } else {
    x = c - '0';
    while (isdigit((c = getchar()))) x = x * 10 + c - '0';
  }
  return x;
}
inline double &RF(double &x) {
  char c;
  while ((c = getchar()), c != '-' && c != '.' && !isdigit(c))
    ;
  if (c == '-')
    if ((c = getchar()) == '.') {
      x = 0;
      double l = 1;
      while (isdigit((c = getchar()))) l /= 10, x = x * 10 + '0' - c;
      x *= l;
    } else {
      x = '0' - c;
      while (isdigit((c = getchar()))) x = x * 10 + '0' - c;
      if (c == '.') {
        double l = 1;
        while (isdigit((c = getchar()))) l /= 10, x = x * 10 + '0' - c;
        x *= l;
      }
    }
  else if (c == '.') {
    x = 0;
    double l = 1;
    while (isdigit((c = getchar()))) l /= 10, x = x * 10 + c - '0';
    x *= l;
  } else {
    x = c - '0';
    while (isdigit((c = getchar()))) x = x * 10 + c - '0';
    if (c == '.') {
      double l = 1;
      while (isdigit((c = getchar()))) l /= 10, x = x * 10 + c - '0';
      x *= l;
    }
  }
  return x;
}
inline char *RS(char *s) {
  scanf("%s", s);
  return s;
}
int last_ans;
int Case;
template <class T>
inline void OT(const T &x) {
  printf("%d\n", x);
}
const int N = int(1e3) + 9;
int col[N][N];
int n, k, c;
void gao(vector<int> &V, int c) {
  if (c == 1) {
    for (int i = 0; i < int((V).size()); ++i)
      for (int j = i + 1; j < int((V).size()); ++j) {
        col[V[i]][V[j]] = 1;
        col[V[j]][V[i]] = 1;
      }
    return;
  }
  vector<vector<int> > VV;
  VV.resize(k);
  int vi = 0;
  int vn = ceil(int((V).size()), k);
  for (int i = 0; i < int((V).size()); ++i) {
    VV[vi].push_back(V[i]);
    if (int((VV[vi]).size()) == vn) ++vi;
  }
  for (int i = 0; i < k; ++i)
    for (int j = i + 1; j < k; ++j) {
      for (auto vi : VV[i])
        for (auto vj : VV[j]) {
          col[vi][vj] = c;
          col[vj][vi] = c;
        }
    }
  --c;
  for (int i = 0; i < k; ++i)
    if (int((VV[i]).size())) gao(VV[i], c);
}
int main() {
  RD(n, k);
  int c = (int)ceil(log(n) / log(k));
  cout << c << endl;
  vector<int> V;
  for (int i = 0; i < n; ++i) V.push_back(i);
  gao(V, c);
  for (int i = 0; i < n; ++i)
    for (int j = i + 1; j < n; ++j) printf("%d ", col[i][j]);
}

### Prompt

Develop a solution in Cpp to the problem described below:

Even if you just leave them be, they will fall to pieces all by themselves. So, someone has to protect them, right?

You find yourself playing with Teucer again in the city of Liyue. As you take the eccentric little kid around, you notice something interesting about the structure of the city.

Liyue can be represented as a directed graph containing n nodes. Nodes are labeled from 1 to n. There is a directed edge from node a to node b if and only if a < b.

A path between nodes a and b is defined as a sequence of edges such that you can start at a, travel along all of these edges in the corresponding direction, and end at b. The length of a path is defined by the number of edges. A rainbow path of length x is defined as a path in the graph such that there exists at least 2 distinct colors among the set of x edges.

Teucer's favorite number is k. You are curious about the following scenario: If you were to label each edge with a color, what is the minimum number of colors needed to ensure that all paths of length k or longer are rainbow paths?

Teucer wants to surprise his older brother with a map of Liyue. He also wants to know a valid coloring of edges that uses the minimum number of colors. Please help him with this task!

Input

The only line of input contains two integers n and k (2 ≤ k < n ≤ 1000). 

Output

On the first line, output c, the minimum colors you need to satisfy the above requirements.

On the second line, print a valid edge coloring as an array of (n(n-1))/(2) integers ranging from 1 to c. Exactly c distinct colors should exist in the construction. Print the edges in increasing order by the start node first, then by the second node.

For example, if n=4, the edge colors will correspond to this order of edges: (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)

Examples

Input


5 3


Output


2
1 2 2 2 2 2 2 1 1 1


Input


5 2


Output


3
3 2 2 1 2 2 1 3 1 1 


Input


8 7


Output


2
2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


Input


3 2


Output


2
1 2 2 

Note

The corresponding construction for the first test case looks like this: 

<image> It is impossible to satisfy the constraints with less than 2 colors.

The corresponding construction for the second test case looks like this: 

<image> One can show there exists no construction using less than 3 colors.

### Response

```cpp
#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:36777216")
using namespace std;
template <class T>
inline T &RD(T &);
template <class T>
inline void OT(const T &);
inline long long RD() {
  long long x;
  return RD(x);
}
inline double &RF(double &);
inline double RF() {
  double x;
  return RF(x);
}
inline char *RS(char *s);
inline char &RC(char &c);
inline char RC();
inline char &RC(char &c) {
  scanf(" %c", &c);
  return c;
}
inline char RC() {
  char c;
  return RC(c);
}
template <class T>
inline T &RDD(T &);
inline long long RDD() {
  long long x;
  return RDD(x);
}
template <class T0, class T1>
inline T0 &RD(T0 &x0, T1 &x1) {
  RD(x0), RD(x1);
  return x0;
}
template <class T0, class T1, class T2>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2) {
  RD(x0), RD(x1), RD(x2);
  return x0;
}
template <class T0, class T1, class T2, class T3>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3) {
  RD(x0), RD(x1), RD(x2), RD(x3);
  return x0;
}
template <class T0, class T1, class T2, class T3, class T4>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4) {
  RD(x0), RD(x1), RD(x2), RD(x3), RD(x4);
  return x0;
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5) {
  RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5);
  return x0;
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline T0 &RD(T0 &x0, T1 &x1, T2 &x2, T3 &x3, T4 &x4, T5 &x5, T6 &x6) {
  RD(x0), RD(x1), RD(x2), RD(x3), RD(x4), RD(x5), RD(x6);
  return x0;
}
template <class T0, class T1>
inline void OT(const T0 &x0, const T1 &x1) {
  OT(x0), OT(x1);
}
template <class T0, class T1, class T2>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2) {
  OT(x0), OT(x1), OT(x2);
}
template <class T0, class T1, class T2, class T3>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3) {
  OT(x0), OT(x1), OT(x2), OT(x3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3,
               const T4 &x4) {
  OT(x0), OT(x1), OT(x2), OT(x3), OT(x4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3,
               const T4 &x4, const T5 &x5) {
  OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void OT(const T0 &x0, const T1 &x1, const T2 &x2, const T3 &x3,
               const T4 &x4, const T5 &x5, const T6 &x6) {
  OT(x0), OT(x1), OT(x2), OT(x3), OT(x4), OT(x5), OT(x6);
}
inline char &RC(char &a, char &b) {
  RC(a), RC(b);
  return a;
}
inline char &RC(char &a, char &b, char &c) {
  RC(a), RC(b), RC(c);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d) {
  RC(a), RC(b), RC(c), RC(d);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d, char &e) {
  RC(a), RC(b), RC(c), RC(d), RC(e);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d, char &e, char &f) {
  RC(a), RC(b), RC(c), RC(d), RC(e), RC(f);
  return a;
}
inline char &RC(char &a, char &b, char &c, char &d, char &e, char &f, char &g) {
  RC(a), RC(b), RC(c), RC(d), RC(e), RC(f), RC(g);
  return a;
}
inline double &RF(double &a, double &b) {
  RF(a), RF(b);
  return a;
}
inline double &RF(double &a, double &b, double &c) {
  RF(a), RF(b), RF(c);
  return a;
}
inline double &RF(double &a, double &b, double &c, double &d) {
  RF(a), RF(b), RF(c), RF(d);
  return a;
}
inline double &RF(double &a, double &b, double &c, double &d, double &e) {
  RF(a), RF(b), RF(c), RF(d), RF(e);
  return a;
}
inline double &RF(double &a, double &b, double &c, double &d, double &e,
                  double &f) {
  RF(a), RF(b), RF(c), RF(d), RF(e), RF(f);
  return a;
}
inline double &RF(double &a, double &b, double &c, double &d, double &e,
                  double &f, double &g) {
  RF(a), RF(b), RF(c), RF(d), RF(e), RF(f), RF(g);
  return a;
}
inline void RS(char *s1, char *s2) { RS(s1), RS(s2); }
inline void RS(char *s1, char *s2, char *s3) { RS(s1), RS(s2), RS(s3); }
template <class T0, class T1>
inline T0 &RDD(T0 &a, T1 &b) {
  RDD(a), RDD(b);
  return a;
}
template <class T0, class T1, class T2>
inline T1 &RDD(T0 &a, T1 &b, T2 &c) {
  RDD(a), RDD(b), RDD(c);
  return a;
}
template <class T>
inline void RST(T &A) {
  memset(A, 0, sizeof(A));
}
template <class T>
inline void FLC(T &A, int x) {
  memset(A, x, sizeof(A));
}
template <class T>
inline void CLR(T &A) {
  A.clear();
}
template <class T0, class T1>
inline void RST(T0 &A0, T1 &A1) {
  RST(A0), RST(A1);
}
template <class T0, class T1, class T2>
inline void RST(T0 &A0, T1 &A1, T2 &A2) {
  RST(A0), RST(A1), RST(A2);
}
template <class T0, class T1, class T2, class T3>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3) {
  RST(A0), RST(A1), RST(A2), RST(A3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4) {
  RST(A0), RST(A1), RST(A2), RST(A3), RST(A4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5) {
  RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void RST(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6) {
  RST(A0), RST(A1), RST(A2), RST(A3), RST(A4), RST(A5), RST(A6);
}
template <class T0, class T1>
inline void FLC(T0 &A0, T1 &A1, int x) {
  FLC(A0, x), FLC(A1, x);
}
template <class T0, class T1, class T2>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x);
}
template <class T0, class T1, class T2, class T3>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void FLC(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6, int x) {
  FLC(A0, x), FLC(A1, x), FLC(A2, x), FLC(A3, x), FLC(A4, x), FLC(A5, x),
      FLC(A6, x);
}
template <class T>
inline void CLR(priority_queue<T> &Q) {
  while (!Q.empty()) Q.pop();
}
template <class T>
inline void CLR(stack<T> &S) {
  while (!S.empty()) S.pop();
}
template <class T>
inline void CLR(queue<T> &Q) {
  while (!Q.empty()) Q.pop();
}
template <class T0, class T1>
inline void CLR(T0 &A0, T1 &A1) {
  CLR(A0), CLR(A1);
}
template <class T0, class T1, class T2>
inline void CLR(T0 &A0, T1 &A1, T2 &A2) {
  CLR(A0), CLR(A1), CLR(A2);
}
template <class T0, class T1, class T2, class T3>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3);
}
template <class T0, class T1, class T2, class T3, class T4>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4);
}
template <class T0, class T1, class T2, class T3, class T4, class T5>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5);
}
template <class T0, class T1, class T2, class T3, class T4, class T5, class T6>
inline void CLR(T0 &A0, T1 &A1, T2 &A2, T3 &A3, T4 &A4, T5 &A5, T6 &A6) {
  CLR(A0), CLR(A1), CLR(A2), CLR(A3), CLR(A4), CLR(A5), CLR(A6);
}
template <class T>
inline void CLR(T &A, int n) {
  for (int i = 0; i < n; ++i) CLR(A[i]);
}
template <class T>
inline bool EPT(T &a) {
  return a.empty();
}
template <class T>
inline T &SRT(T &A) {
  sort(A.begin(), A.end());
  return A;
}
template <class T, class C>
inline T &SRT(T &A, C cmp) {
  sort(A.begin(), A.end(), cmp);
  return A;
}
template <class T>
inline T &RVS(T &A) {
  reverse(A.begin(), A.end());
  return A;
}
template <class T>
inline T &UNQQ(T &A) {
  A.resize(unique(A.begin(), A.end()) - A.begin());
  return A;
}
template <class T>
inline T &UNQ(T &A) {
  SRT(A);
  return UNQQ(A);
}
template <class T, class C>
inline T &UNQ(T &A, C cmp) {
  SRT(A, cmp);
  return UNQQ(A);
}
const int MOD = int(1e9) + 7;
const int INF = 0x3f3f3f3f;
const long long INFF = 0x3f3f3f3f3f3f3f3fLL;
const double EPS = 1e-9;
const double OO = 1e20;
const double PI = acos(-1.0);
const int dx[] = {-1, 1, 0, 0};
const int dy[] = {0, 0, 1, -1};
template <class T>
inline bool checkMin(T &a, const T b) {
  return b < a ? a = b, 1 : 0;
}
template <class T>
inline bool checkMax(T &a, const T b) {
  return a < b ? a = b, 1 : 0;
}
template <class T, class C>
inline bool checkUpd(T &a, const T b, C c) {
  return c(b, a) ? a = b, 1 : 0;
}
template <class T>
inline T min(T a, T b, T c) {
  return min(min(a, b), c);
}
template <class T>
inline T max(T a, T b, T c) {
  return max(max(a, b), c);
}
template <class T>
inline T min(T a, T b, T c, T d) {
  return min(min(a, b), min(c, d));
}
template <class T>
inline T max(T a, T b, T c, T d) {
  return max(max(a, b), max(c, d));
}
template <class T>
inline T min(T a, T b, T c, T d, T e) {
  return min(min(min(a, b), min(c, d)), e);
}
template <class T>
inline T max(T a, T b, T c, T d, T e) {
  return max(max(max(a, b), max(c, d)), e);
}
template <class T>
inline T sqr(T a) {
  return a * a;
}
template <class T>
inline T cub(T a) {
  return a * a * a;
}
template <class T>
inline T ceil(T x, T y) {
  return (x - 1) / y + 1;
}
template <class T>
T abs(T x) {
  return x > 0 ? x : -x;
}
inline int sgn(double x) { return x < -EPS ? -1 : x > EPS; }
inline int sgn(double x, double y) { return sgn(x - y); }
inline double cos(double a, double b, double c) {
  return (sqr(a) + sqr(b) - sqr(c)) / (2 * a * b);
}
inline double cot(double x) { return 1. / tan(x); };
inline double sec(double x) { return 1. / cos(x); };
inline double csc(double x) { return 1. / sin(x); };
namespace CG {
inline double dist2(double x, double y) { return sqr(x) + sqr(y); }
struct Po {
  double x, y;
  Po(double x = 0, double y = 0) : x(x), y(y) {}
  void in() { RF(x, y); }
  void out() { printf("(%.2f,%.2f)", x, y); }
  inline friend istream &operator>>(istream &i, Po &p) {
    return i >> p.x >> p.y;
  }
  inline friend ostream &operator<<(ostream &o, Po p) {
    return o << "(" << p.x << ", " << p.y << ")";
  }
  Po operator-() const { return Po(-x, -y); }
  Po &operator+=(const Po &p) {
    x += p.x, y += p.y;
    return *this;
  }
  Po &operator-=(const Po &p) {
    x -= p.x, y -= p.y;
    return *this;
  }
  Po &operator*=(double k) {
    x *= k, y *= k;
    return *this;
  }
  Po &operator/=(double k) {
    x /= k, y /= k;
    return *this;
  }
  Po &operator*=(const Po &p) { return *this = *this * p; }
  Po &operator/=(const Po &p) { return *this = *this / p; }
  Po operator+(const Po &p) const { return Po(x + p.x, y + p.y); }
  Po operator-(const Po &p) const { return Po(x - p.x, y - p.y); }
  Po operator*(double k) const { return Po(x * k, y * k); }
  Po operator/(double k) const { return Po(x / k, y / k); }
  Po operator*(const Po &p) const {
    return Po(x * p.x - y * p.y, y * p.x + x * p.y);
  }
  Po operator/(const Po &p) const {
    return Po(x * p.x + y * p.y, y * p.x - x * p.y) / p.len2();
  }
  bool operator==(const Po &p) const { return !sgn(x, p.x) && !sgn(y, p.y); };
  bool operator!=(const Po &p) const { return sgn(x, p.x) || sgn(y, p.y); }
  bool operator<(const Po &p) const {
    return sgn(x, p.x) < 0 || !sgn(x, p.x) && sgn(y, p.y) < 0;
  }
  bool operator<=(const Po &p) const {
    return sgn(x, p.x) < 0 || !sgn(x, p.x) && sgn(y, p.y) <= 0;
  }
  bool operator>(const Po &p) const { return !(*this <= p); }
  bool operator>=(const Po &p) const { return !(*this < p); }
  double len2() const { return dist2(x, y); }
  double len() const { return sqrt(len2()); }
  double arg() const { return atan2(y, x); }
  Po &_1() { return *this /= len(); }
  Po &conj() {
    y = -y;
    return *this;
  }
  Po &lt() {
    swap(x, y), x = -x;
    return *this;
  }
  Po &rt() {
    swap(x, y), y = -y;
    return *this;
  }
  Po &rot(double a, const Po &o = Po()) {
    *this -= o;
    *this *= Po(cos(a), sin(a));
    return *this += o;
  }
  inline int q() const { return (y > 0 || y == 0 && x >= 0) ? 0 : 1; }
};
inline double dot(double x1, double y1, double x2, double y2) {
  return x1 * x2 + y1 * y2;
}
inline double dot(const Po &a, const Po &b) { return dot(a.x, a.y, b.x, b.y); }
inline double dot(const Po &p0, const Po &p1, const Po &p2) {
  return dot(p1 - p0, p2 - p0);
}
inline double det(double x1, double y1, double x2, double y2) {
  return x1 * y2 - x2 * y1;
}
inline double det(const Po &a, const Po &b) { return det(a.x, a.y, b.x, b.y); }
inline double det(const Po &p0, const Po &p1, const Po &p2) {
  return det(p1 - p0, p2 - p0);
}
inline double ang(const Po &p0, const Po &p1) {
  return acos(dot(p0, p1) / p0.len() / p1.len());
}
inline double ang(const Po &p0, const Po &p1, const Po &p2) {
  return ang(p1 - p0, p2 - p0);
}
inline double ang(const Po &p0, const Po &p1, const Po &p2, const Po &p3) {
  return ang(p1 - p0, p3 - p2);
}
inline double dist2(const Po &a, const Po &b) {
  return dist2(a.x - b.x, a.y - b.y);
}
template <class T1, class T2>
inline int dett(const T1 &x, const T2 &y) {
  return sgn(det(x, y));
}
template <class T1, class T2, class T3>
inline int dett(const T1 &x, const T2 &y, const T3 &z) {
  return sgn(det(x, y, z));
}
template <class T1, class T2, class T3, class T4>
inline int dett(const T1 &x, const T2 &y, const T3 &z, const T4 &w) {
  return sgn(det(x, y, z, w));
}
template <class T1, class T2>
inline int dott(const T1 &x, const T2 &y) {
  return sgn(dot(x, y));
}
template <class T1, class T2, class T3>
inline int dott(const T1 &x, const T2 &y, const T3 &z) {
  return sgn(dot(x, y, z));
}
template <class T1, class T2, class T3, class T4>
inline int dott(const T1 &x, const T2 &y, const T3 &z, const T4 &w) {
  return sgn(dot(x, y, z, w));
}
template <class T1, class T2>
inline double arg(const T1 &x, const T2 &y) {
  double a = ang(x, y);
  return ~dett(x, y) ? a : 2 * PI - a;
}
template <class T1, class T2, class T3>
inline double arg(const T1 &x, const T2 &y, const T3 &z) {
  double a = ang(x, y, z);
  return ~dett(x, y, z) ? a : 2 * PI - a;
}
template <class T1, class T2, class T3, class T4>
inline double arg(const T1 &x, const T2 &y, const T3 &z, const T4 &w) {
  double a = ang(x, y, z, w);
  return ~dett(x, y, z, w) ? a : 2 * PI - a;
}
template <class T1, class T2>
inline double dist(const T1 &x, const T2 &y) {
  return sqrt(dist2(x, y));
}
template <class T1, class T2, class T3>
inline double dist(const T1 &x, const T2 &y, const T3 &z) {
  return sqrt(dist2(x, y, z));
}
inline Po _1(Po p) { return p._1(); }
inline Po conj(Po p) { return p.conj(); }
inline Po lt(Po p) { return p.lt(); }
inline Po rt(Po p) { return p.rt(); }
inline Po rot(Po p, double a, const Po &o = Po()) { return p.rot(a, o); }
inline Po operator*(double k, const Po &p) { return p * k; }
inline Po operator/(double k, const Po &p) { return conj(p) * k / p.len2(); }
struct Line {
  Po a, b;
  Line(const Po &a = Po(), const Po &b = Po()) : a(a), b(b) {}
  Line(double x0, double y0, double x1, double y1)
      : a(Po(x0, y0)), b(Po(x1, y1)) {}
  Line(const Line &l) : a(l.a), b(l.b) {}
  Line(double A, double B, double C) {
    C = -C;
    if (!::sgn(A))
      a = Po(0, C / B), b = Po(1, C / B);
    else if (!::sgn(B))
      a = Po(C / A, 0), b = Po(C / A, 1);
    else
      a = Po(0, C / B), b = Po(1, (C - A) / B);
  }
  void in() { a.in(), b.in(); }
  inline friend istream &operator>>(istream &i, Line &p) {
    return i >> p.a >> p.b;
  }
  inline friend ostream &operator<<(ostream &o, Line p) {
    return o << p.a << "-" << p.b;
  }
  Line operator+(const Po &x) const { return Line(a + x, b + x); }
  Line operator-(const Po &x) const { return Line(a - x, b - x); }
  Line operator*(double k) const { return Line(a * k, b * k); }
  Line operator/(double k) const { return Line(a / k, b / k); }
  Po operator*(const Line &) const;
  Po d() const { return b - a; }
  double len2() const { return d().len2(); }
  double len() const { return d().len(); }
  double arg() const { return d().arg(); }
  int sgn(const Po &p) const { return dett(a, b, p); }
  int sgn(const Line &) const;
  bool sameSgn(const Po &p1, const Po &p2) const { return sgn(p1) == sgn(p2); }
  void getEquation(double &K, double &B) const {
    K = ::sgn(a.x, b.x) ? (b.y - a.y) / (b.x - a.x) : OO;
    B = a.y - K * a.x;
  }
  void getEquation(double &A, double &B, double &C) const {
    A = a.y - b.y, B = b.x - a.x, C = det(a, b);
  }
  Line &push(double r) {
    Po v = d()._1().lt() * r;
    a += v, b += v;
    return *this;
  }
};
inline double dot(const Line &l1, const Line &l2) {
  return dot(l1.d(), l2.d());
}
inline double dot(const Line &l, const Po &p) { return dot(l.a, l.b, p); }
inline double dot(const Po &p, const Line &l) { return dot(p, l.a, l.b); }
inline double det(const Line &l1, const Line &l2) {
  return det(l1.d(), l2.d());
}
inline double det(const Line &l, const Po &p) { return det(l.a, l.b, p); }
inline double det(const Po &p, const Line &l) { return det(p, l.a, l.b); }
inline double ang(const Line &l0, const Line &l1) {
  return ang(l0.d(), l1.d());
}
inline double ang(const Line &l, const Po &p) { return ang(l.a, l.b, p); }
inline double ang(const Po &p, const Line &l) { return ang(p, l.a, l.b); }
inline int Line::sgn(const Line &l) const { return dett(*this, l); }
inline Po Line::operator*(const Line &l) const {
  return a + d() * det(a, l) / det(*this, l);
}
inline Po operator&(const Po &p, const Line &l) {
  return l * Line(p, p + l.d().lt());
}
inline Po operator%(const Po &p, const Line &l) { return p & l * 2 - p; }
inline Line push(Line l, double r) { return l.push(r); }
struct Seg : public Line {
  Seg(const Po &a = Po(), const Po &b = Po()) : Line(a, b) {}
  Seg(double x0, double y0, double x1, double y1) : Line(x0, y0, x1, y1) {}
  Seg(const Line &l) : Line(l) {}
  Seg(const Po &a, double alpha) : Line(a, alpha) {}
  Seg(double A, double B, double C) : Line(A, B, C) {}
  inline int sgn(const Po &p) const;
  inline int sgn(const Line &l) const;
  inline bool qrt(const Seg &l) const;
  inline int sgn(const Seg &l) const;
};
inline int Seg::sgn(const Po &p) const {
  if (dett(p, a, b)) return -1;
  if (a == p || b == p) return 0;
  return -dott(p, a, b);
}
inline int Seg::sgn(const Line &l) const { return sgn(*this * l); }
inline bool Seg::qrt(const Seg &l) const {
  return min(a.x, b.x) <= max(l.a.x, l.b.x) &&
         min(l.a.x, l.b.x) <= max(a.x, b.x) &&
         min(a.y, b.y) <= max(l.a.y, l.b.y) &&
         min(l.a.y, l.b.y) <= max(a.y, b.y);
}
inline int Seg::sgn(const Seg &l) const {
  if (!qrt(l)) return -1;
  int d1 = dett(a, b, l.a), d2 = dett(a, b, l.b), d3 = dett(l.a, l.b, a),
      d4 = dett(l.a, l.b, b);
  if ((d1 ^ d2) == -2 && (d3 ^ d4) == -2) return 1;
  return ((!d1 && dott(l.a - a, l.a - b) <= 0) ||
          (!d2 && dott(l.b - a, l.b - b) <= 0) ||
          (!d3 && dott(a - l.a, a - l.b) <= 0) ||
          (!d4 && dott(b - l.a, b - l.b) <= 0))
             ? 0
             : -1;
}
inline double dist2(const Line &l, const Po &p) {
  return sqr(fabs(det(l.d(), p - l.a))) / l.len2();
}
inline double dist2(const Line &l1, const Line &l2) {
  return dett(l1, l2) ? 0 : dist2(l1, l2.a);
}
inline double dist2(const Seg &l, const Po &p) {
  Po pa = p - l.a, pb = p - l.b;
  if (dott(l.d(), pa) <= 0) return pa.len2();
  if (dott(l.d(), pb) >= 0) return pb.len2();
  return dist2(Line(l), p);
}
inline double dist2(const Seg &s, const Line &l) {
  Po v1 = s.a - l.a, v2 = s.b - l.a;
  double d1 = det(l.d(), v1), d2 = det(l.d(), v2);
  return sgn(d1) != sgn(d2) ? 0 : sqr(min(fabs(d1), fabs(d2))) / l.len2();
}
inline double dist2(const Seg &l1, const Seg &l2) {
  if (~l1.sgn(l2))
    return 0;
  else
    return min(dist2(l2, l1.a), dist2(l2, l1.b), dist2(l1, l2.a),
               dist2(l1, l2.b));
}
template <class T1, class T2>
inline double dist2(const T1 &a, const T2 &b) {
  return dist2(b, a);
}
}  // namespace CG
using namespace CG;
template <class T>
inline T &RD(T &x) {
  char c;
  while (!isdigit((c = getchar())))
    ;
  x = c - '0';
  while (isdigit((c = getchar()))) x = x * 10 + c - '0';
  return x;
}
template <class T>
inline T &RDD(T &x) {
  char c;
  while ((c = getchar()), c != '-' && !isdigit(c))
    ;
  if (c == '-') {
    x = '0' - (c = getchar());
    while (isdigit((c = getchar()))) x = x * 10 + '0' - c;
  } else {
    x = c - '0';
    while (isdigit((c = getchar()))) x = x * 10 + c - '0';
  }
  return x;
}
inline double &RF(double &x) {
  char c;
  while ((c = getchar()), c != '-' && c != '.' && !isdigit(c))
    ;
  if (c == '-')
    if ((c = getchar()) == '.') {
      x = 0;
      double l = 1;
      while (isdigit((c = getchar()))) l /= 10, x = x * 10 + '0' - c;
      x *= l;
    } else {
      x = '0' - c;
      while (isdigit((c = getchar()))) x = x * 10 + '0' - c;
      if (c == '.') {
        double l = 1;
        while (isdigit((c = getchar()))) l /= 10, x = x * 10 + '0' - c;
        x *= l;
      }
    }
  else if (c == '.') {
    x = 0;
    double l = 1;
    while (isdigit((c = getchar()))) l /= 10, x = x * 10 + c - '0';
    x *= l;
  } else {
    x = c - '0';
    while (isdigit((c = getchar()))) x = x * 10 + c - '0';
    if (c == '.') {
      double l = 1;
      while (isdigit((c = getchar()))) l /= 10, x = x * 10 + c - '0';
      x *= l;
    }
  }
  return x;
}
inline char *RS(char *s) {
  scanf("%s", s);
  return s;
}
int last_ans;
int Case;
template <class T>
inline void OT(const T &x) {
  printf("%d\n", x);
}
const int N = int(1e3) + 9;
int col[N][N];
int n, k, c;
void gao(vector<int> &V, int c) {
  if (c == 1) {
    for (int i = 0; i < int((V).size()); ++i)
      for (int j = i + 1; j < int((V).size()); ++j) {
        col[V[i]][V[j]] = 1;
        col[V[j]][V[i]] = 1;
      }
    return;
  }
  vector<vector<int> > VV;
  VV.resize(k);
  int vi = 0;
  int vn = ceil(int((V).size()), k);
  for (int i = 0; i < int((V).size()); ++i) {
    VV[vi].push_back(V[i]);
    if (int((VV[vi]).size()) == vn) ++vi;
  }
  for (int i = 0; i < k; ++i)
    for (int j = i + 1; j < k; ++j) {
      for (auto vi : VV[i])
        for (auto vj : VV[j]) {
          col[vi][vj] = c;
          col[vj][vi] = c;
        }
    }
  --c;
  for (int i = 0; i < k; ++i)
    if (int((VV[i]).size())) gao(VV[i], c);
}
int main() {
  RD(n, k);
  int c = (int)ceil(log(n) / log(k));
  cout << c << endl;
  vector<int> V;
  for (int i = 0; i < n; ++i) V.push_back(i);
  gao(V, c);
  for (int i = 0; i < n; ++i)
    for (int j = i + 1; j < n; ++j) printf("%d ", col[i][j]);
}

```