Let's call the roundness of the number the number of zeros to which it ends.

You have an array of n numbers. You need to choose a subset of exactly k numbers so that the roundness of the product of the selected numbers will be maximum possible.

Input

The first line contains two integer numbers n and k (1 ≤ n ≤ 200, 1 ≤ k ≤ n).

The second line contains n space-separated integer numbers a1, a2, ..., an (1 ≤ ai ≤ 1018).

Output

Print maximal roundness of product of the chosen subset of length k.

Examples

Input

3 2
50 4 20


Output

3


Input

5 3
15 16 3 25 9


Output

3


Input

3 3
9 77 13


Output

0

Note

In the first example there are 3 subsets of 2 numbers. [50, 4] has product 200 with roundness 2, [4, 20] — product 80, roundness 1, [50, 20] — product 1000, roundness 3.

In the second example subset [15, 16, 25] has product 6000, roundness 3.

In the third example all subsets has product with roundness 0.
#include <bits/stdc++.h>
using namespace std;
const int e = 0x3f3f3f3f;
int n, k, m, f[201][5001];
int main() {
  memset(f, -e, sizeof(f));
  scanf("%d%d", &n, &k);
  f[0][0] = 0;
  m = 0;
  for (register int i = (1); i <= n; ++i) {
    long long x;
    int u = 0, v = 0;
    scanf("%I64d", &x);
    while (x % 2 == 0) {
      x /= 2;
      ++u;
    }
    while (x % 5 == 0) {
      x /= 5;
      ++v;
    }
    m += v;
    for (register int j = (k); j >= 1; --j)
      for (register int l = (v); l <= m; ++l)
        f[j][l] = max(f[j][l], f[j - 1][l - v] + u);
  }
  int kq = 0;
  for (register int i = (1); i <= m; ++i) kq = max(kq, min(i, f[k][i]));
  printf("%d", kq);
  return 0;
}
