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;
long long int num[210];
int a[210];
int b[210];
int dp[200000][210];
int main() {
  int n, k;
  scanf("%d%d", &n, &k);
  for (int i = 0; i < n; i++) scanf("%I64d", &num[i]);
  for (int i = 0; i < n; i++) {
    while (num[i] >= 2 && num[i] % 2 == 0) num[i] /= 2, a[i]++;
    while (num[i] >= 5 && num[i] % 5 == 0) num[i] /= 5, b[i]++;
  }
  int V = 0;
  for (int i = 0; i < n; i++) V += a[i];
  for (int i = 0; i <= V; i++)
    for (int j = 0; j <= k; j++) dp[i][j] = INT_MIN;
  dp[0][0] = 0;
  for (int i = 0; i < n; i++) {
    for (int w = k; w >= 1; w--) {
      for (int j = a[i]; j <= V; j++) {
        dp[j][w] = max(dp[j][w], dp[j - a[i]][w - 1] + b[i]);
      }
    }
  }
  int ans = 0;
  for (int i = 1; i <= V; i++) {
    ans = max(ans, min(i, dp[i][k]));
  }
  printf("%d\n", ans);
  return 0;
}
