#include <bits/stdc++.h>
using namespace std;
template <class T, class first>
inline bool checkbit(T a, first pos) {
  T t = 1;
  return ((a & (t << pos)) > 0);
}
template <class T, class first>
inline T setbit(T a, first pos) {
  T t = 1;
  return (a | (t << pos));
}
template <class T, class first>
inline T resetbit(T a, first pos) {
  T t = 1;
  return (a & (~(t << pos)));
}
template <class T, class first>
inline T togglebit(T a, first pos) {
  T t = 1;
  return (a ^ (t << pos));
}
template <typename T>
T POW(T B, T printf) {
  if (printf == 0) return 1;
  if (printf & 1)
    return B * POW(B, printf - 1);
  else
    return (POW(B, printf / 2) * POW(B, printf / 2));
}
template <typename T>
T Bigmod(T base, T power, T mod) {
  T ret = 1;
  while (power) {
    if (power & 1) ret = (ret * base) % mod;
    base = (base * base) % mod;
    power >>= 1;
  }
  return ret;
}
template <typename T>
T ModInverse(T number, T mod) {
  return Bigmod(number, mod - 2, mod);
}
template <typename T>
T GCD(T a, T b) {
  if (a < 0) return GCD(-a, b);
  if (b < 0) return GCD(a, -b);
  return (b == 0) ? a : GCD(b, a % b);
}
template <typename T>
T LCM(T a, T b) {
  if (a < 0) return LCM(-a, b);
  if (b < 0) return LCM(a, -b);
  return a * (b / GCD(a, b));
}
template <typename T>
T EUCLIDE(T a, T b, T &x, T &y) {
  if (a < 0) {
    T d = euclide(-a, b, x, y);
    x = -x;
    return d;
  }
  if (b < 0) {
    T d = euclide(a, -b, x, y);
    y = -y;
    return d;
  }
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  } else {
    T d = euclide(b, a % b, x, y);
    T t = x;
    x = y;
    y = t - (a / b) * y;
    return d;
  }
}
template <typename T>
T ABS(T a) {
  if (a < 0)
    return -a;
  else
    return a;
}
double DEG(double x) { return (180.0 * x) / ((2.0 * acos(0.0))); }
double RAD(double x) { return (x * (double)(2.0 * acos(0.0))) / (180.0); }
template <typename T>
double DIS(T x1, T y1, T x2, T y2) {
  return sqrt((double)((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)));
}
template <typename T>
T ANGLE(T x1, T y1, T x2, T y2) {
  return atan(double(y1 - y2) / double(x1 - x2));
}
template <typename T>
long long isLeft(T a, T b, T c) {
  return (c.x - a.x) * (b.y - a.y) - (b.x - a.x) * (c.y - a.y);
}
template <class T>
inline bool setmin(T &a, T b) {
  return a > b ? a = b, true : false;
}
template <class T>
inline bool setmax(T &a, T b) {
  return a < b ? a = b, true : false;
}
void P_ARR(int *ar, int a, int b) {
  if (a > b) swap(a, b);
  if (a <= b) cout << ar[a];
  for (int i = a + 1; i <= b; i++) cout << " " << ar[i];
  cout << endl;
}
template <typename T>
T in() {
  char ch;
  T n = 0;
  bool ng = false;
  while (1) {
    ch = getchar();
    if (ch == '-') {
      ng = true;
      ch = getchar();
      break;
    }
    if (ch >= '0' && ch <= '9') break;
  }
  while (1) {
    n = n * 10 + (ch - '0');
    ch = getchar();
    if (ch < '0' || ch > '9') break;
  }
  return (ng ? -n : n);
}
int ar[70];
long long dp[70][2][70];
int len;
int p;
long long call(int pos, int choto, int cnt) {
  if (cnt > len) return 0;
  if (pos == len) return (cnt == p);
  long long &ret = dp[pos][choto][cnt];
  if (ret != -1) return ret;
  ret = 0;
  int high = (choto) ? 1 : ar[pos];
  for (int i = 0; i <= high; i++)
    ret += call(pos + 1, (choto || (i < high)), cnt + i);
  return ret;
}
int main() {
  long long N, T;
  cin >> N >> T;
  long long v = 1;
  while (v < T) {
    p++;
    v *= 2;
  }
  if (v > T) {
    printf("%d\n", 0);
    return 0;
  }
  p = p + 1;
  N++;
  while (N) ar[len++] = N % 2, N /= 2;
  reverse(ar, ar + len);
  memset(dp, -1, sizeof dp);
  printf("%lld\n", call(0, 0, 0) - (T == 1));
  return 0;
}

### Prompt

Please formulate a cpp solution to the following problem:

Maxim loves to fill in a matrix in a special manner. Here is a pseudocode of filling in a matrix of size (m + 1) × (m + 1):

<image>

Maxim asks you to count, how many numbers m (1 ≤ m ≤ n) are there, such that the sum of values in the cells in the row number m + 1 of the resulting matrix equals t.

Expression (x xor y) means applying the operation of bitwise excluding "OR" to numbers x and y. The given operation exists in all modern programming languages. For example, in languages C++ and Java it is represented by character "^", in Pascal — by "xor".

Input

A single line contains two integers n and t (1 ≤ n, t ≤ 1012, t ≤ n + 1).

Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.

Output

In a single line print a single integer — the answer to the problem. 

Examples

Input

1 1


Output

1


Input

3 2


Output

1


Input

3 3


Output

0


Input

1000000000000 1048576


Output

118606527258

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <class T, class first>
inline bool checkbit(T a, first pos) {
  T t = 1;
  return ((a & (t << pos)) > 0);
}
template <class T, class first>
inline T setbit(T a, first pos) {
  T t = 1;
  return (a | (t << pos));
}
template <class T, class first>
inline T resetbit(T a, first pos) {
  T t = 1;
  return (a & (~(t << pos)));
}
template <class T, class first>
inline T togglebit(T a, first pos) {
  T t = 1;
  return (a ^ (t << pos));
}
template <typename T>
T POW(T B, T printf) {
  if (printf == 0) return 1;
  if (printf & 1)
    return B * POW(B, printf - 1);
  else
    return (POW(B, printf / 2) * POW(B, printf / 2));
}
template <typename T>
T Bigmod(T base, T power, T mod) {
  T ret = 1;
  while (power) {
    if (power & 1) ret = (ret * base) % mod;
    base = (base * base) % mod;
    power >>= 1;
  }
  return ret;
}
template <typename T>
T ModInverse(T number, T mod) {
  return Bigmod(number, mod - 2, mod);
}
template <typename T>
T GCD(T a, T b) {
  if (a < 0) return GCD(-a, b);
  if (b < 0) return GCD(a, -b);
  return (b == 0) ? a : GCD(b, a % b);
}
template <typename T>
T LCM(T a, T b) {
  if (a < 0) return LCM(-a, b);
  if (b < 0) return LCM(a, -b);
  return a * (b / GCD(a, b));
}
template <typename T>
T EUCLIDE(T a, T b, T &x, T &y) {
  if (a < 0) {
    T d = euclide(-a, b, x, y);
    x = -x;
    return d;
  }
  if (b < 0) {
    T d = euclide(a, -b, x, y);
    y = -y;
    return d;
  }
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  } else {
    T d = euclide(b, a % b, x, y);
    T t = x;
    x = y;
    y = t - (a / b) * y;
    return d;
  }
}
template <typename T>
T ABS(T a) {
  if (a < 0)
    return -a;
  else
    return a;
}
double DEG(double x) { return (180.0 * x) / ((2.0 * acos(0.0))); }
double RAD(double x) { return (x * (double)(2.0 * acos(0.0))) / (180.0); }
template <typename T>
double DIS(T x1, T y1, T x2, T y2) {
  return sqrt((double)((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)));
}
template <typename T>
T ANGLE(T x1, T y1, T x2, T y2) {
  return atan(double(y1 - y2) / double(x1 - x2));
}
template <typename T>
long long isLeft(T a, T b, T c) {
  return (c.x - a.x) * (b.y - a.y) - (b.x - a.x) * (c.y - a.y);
}
template <class T>
inline bool setmin(T &a, T b) {
  return a > b ? a = b, true : false;
}
template <class T>
inline bool setmax(T &a, T b) {
  return a < b ? a = b, true : false;
}
void P_ARR(int *ar, int a, int b) {
  if (a > b) swap(a, b);
  if (a <= b) cout << ar[a];
  for (int i = a + 1; i <= b; i++) cout << " " << ar[i];
  cout << endl;
}
template <typename T>
T in() {
  char ch;
  T n = 0;
  bool ng = false;
  while (1) {
    ch = getchar();
    if (ch == '-') {
      ng = true;
      ch = getchar();
      break;
    }
    if (ch >= '0' && ch <= '9') break;
  }
  while (1) {
    n = n * 10 + (ch - '0');
    ch = getchar();
    if (ch < '0' || ch > '9') break;
  }
  return (ng ? -n : n);
}
int ar[70];
long long dp[70][2][70];
int len;
int p;
long long call(int pos, int choto, int cnt) {
  if (cnt > len) return 0;
  if (pos == len) return (cnt == p);
  long long &ret = dp[pos][choto][cnt];
  if (ret != -1) return ret;
  ret = 0;
  int high = (choto) ? 1 : ar[pos];
  for (int i = 0; i <= high; i++)
    ret += call(pos + 1, (choto || (i < high)), cnt + i);
  return ret;
}
int main() {
  long long N, T;
  cin >> N >> T;
  long long v = 1;
  while (v < T) {
    p++;
    v *= 2;
  }
  if (v > T) {
    printf("%d\n", 0);
    return 0;
  }
  p = p + 1;
  N++;
  while (N) ar[len++] = N % 2, N /= 2;
  reverse(ar, ar + len);
  memset(dp, -1, sizeof dp);
  printf("%lld\n", call(0, 0, 0) - (T == 1));
  return 0;
}

```