There is a toy building consisting of n towers. Each tower consists of several cubes standing on each other. The i-th tower consists of h_i cubes, so it has height h_i.

Let's define operation slice on some height H as following: for each tower i, if its height is greater than H, then remove some top cubes to make tower's height equal to H. Cost of one "slice" equals to the total number of removed cubes from all towers.

Let's name slice as good one if its cost is lower or equal to k (k ≥ n).

<image>

Calculate the minimum number of good slices you have to do to make all towers have the same height. Of course, it is always possible to make it so.

Input

The first line contains two integers n and k (1 ≤ n ≤ 2 ⋅ 10^5, n ≤ k ≤ 10^9) — the number of towers and the restriction on slices, respectively.

The second line contains n space separated integers h_1, h_2, ..., h_n (1 ≤ h_i ≤ 2 ⋅ 10^5) — the initial heights of towers.

Output

Print one integer — the minimum number of good slices you have to do to make all towers have the same heigth.

Examples

Input

5 5
3 1 2 2 4


Output

2


Input

4 5
2 3 4 5


Output

2

Note

In the first example it's optimal to make 2 slices. The first slice is on height 2 (its cost is 3), and the second one is on height 1 (its cost is 4).
#include <bits/stdc++.h>
using namespace std;
int dx4[] = {0, 0, -1, 1};
int dy4[] = {-1, 1, 0, 0};
int dx8[] = {0, 0, -1, 1, -1, -1, 1, 1};
int dy8[] = {-1, 1, 0, 0, -1, 1, -1, 1};
int knightx[] = {-1, 1, -2, 2, -2, 2, -1, 1};
int knighty[] = {-2, -2, -1, -1, 1, 1, 2, 2};
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) {
    if (ch < '0' || ch > '9') break;
    n = n * 10 + (ch - '0');
    ch = getchar();
  }
  return (ng ? -n : n);
}
template <typename T>
inline T POW(T B, T P) {
  if (P == 0) return 1;
  if (P & 1)
    return B * POW(B, P - 1);
  else
    return (POW(B, P / 2) * POW(B, P / 2));
}
template <typename T>
inline 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>
inline 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 Bigmod(T base, T power, T MOD) {
  T ret = T(1) % MOD;
  while (power) {
    if (power & 1) ret = (ret * base) % MOD;
    base = (base * base) % MOD;
    power >>= 1;
  }
  return ret;
}
bool isVowel(char ch) {
  ch = toupper(ch);
  if (ch == 'A' || ch == 'U' || ch == 'I' || ch == 'O' || ch == 'E')
    return true;
  return false;
}
template <typename T>
long long isLeft(T a, T b, T c) {
  return (a.x - b.x) * (b.y - c.y) - (b.x - c.x) * (a.y - b.y);
}
template <typename T>
T ModInverse(T number, T MOD) {
  return Bigmod(number, MOD - T(2), MOD);
}
bool isConst(char ch) {
  if (isalpha(ch) && !isVowel(ch)) return true;
  return false;
}
int toInt(string s) {
  int sm;
  stringstream ss(s);
  ss >> sm;
  return sm;
}
bool isPrime(long long val) {
  if (val == 2) return true;
  if (val % 2 == 0 || val == 1) return false;
  long long sqrt_N = (long long)((double)sqrt(val));
  for (long long i = 3; i <= sqrt_N; i += 2) {
    if (val % i == 0) return false;
  }
  return true;
}
template <class T>
string convert(T _input) {
  stringstream blah;
  blah << _input;
  return blah.str();
}
bool valid(int r, int c, int x, int y) {
  if (x >= 1 && x <= r && y >= 1 && y <= c) return 1;
  return 0;
}
map<string, long long> month;
void Month() {
  month["January"] = 1, month["February"] = 2, month["March"] = 3,
  month["April"] = 4, month["May"] = 5, month["June"] = 6;
  month["July"] = 7, month["August"] = 8, month["September"] = 9,
  month["October"] = 10, month["November"] = 11, month["December"] = 12;
}
bool Check(int val, int pos) { return bool(val & (1 << pos)); }
int Set(int val, int pos) { return val | (1 << pos); }
int Reset(int val, int pos) { return val & (~(1 << pos)); }
int Flip(int val, int pos) { return val ^ (1 << pos); }
long long n, m, caseno;
long long a[200005];
long long b[200005];
long long Fun() {
  long long left = 0, right = n, mid, res = 0;
  while (left <= right) {
    mid = left + ((right - left) >> 1);
    if ((mid * (mid - 1)) / 2 >= m) {
      res = mid;
      right = mid - 1;
    } else
      left = mid + 1;
  }
  return res;
}
int main() {
  long long i, j, t;
  n = in<long long>(), m = in<long long>();
  long long Mn = LLONG_MAX;
  for (i = 1; i <= n; i++) {
    a[i] = in<long long>();
    Mn = min(Mn, a[i]);
  }
  long long Mx = 0LL;
  for (i = 1; i <= n; i++) {
    a[i] -= Mn;
    Mx = max(Mx, a[i]);
  }
  for (i = 1; i <= n; i++) {
    if (a[i]) {
      b[1]++;
      b[a[i] + 1]--;
    }
  }
  long long d = 0;
  for (i = 1; i <= Mx; i++) {
    d += b[i];
    a[i] = d;
  }
  long long tot = 0;
  long long res = 0;
  for (i = Mx; i >= 1; i--) {
    if (tot + a[i] > m) {
      tot = a[i];
      res++;
      if (i == 1) res++;
    } else {
      tot += a[i];
      if (i == 1) res++;
    }
  }
  printf("%lld\n", res);
  return 0;
}
