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;
int n, m, allcnt, dp[205][12005], cnt2, cnt5, ans;
long long uu;
int main() {
  cin >> n >> m;
  memset(dp, 0x80, sizeof(dp));
  dp[0][0] = 0;
  for (int i = 1; i <= n; i++) {
    cin >> uu;
    cnt2 = cnt5 = 0;
    while (uu % 2 == 0) {
      cnt2++;
      uu /= 2;
    }
    while (uu % 5 == 0) {
      cnt5++;
      uu /= 5;
    }
    allcnt += cnt2;
    for (int j = min(m, i); j >= 1; j--)
      for (int k = allcnt; k >= cnt2; k--)
        dp[j][k] = max(dp[j - 1][k - cnt2] + cnt5, dp[j][k]);
  }
  for (int i = 1; i <= allcnt; i++) ans = max(ans, min(dp[m][i], i));
  cout << ans << endl;
  return 0;
}
