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 N = 205;
int x, y;
int dp[N][N * 26], dp2[N][N * 26];
bool poss[N][N * 26], poss2[N][N * 26];
long long a;
int main() {
  int n, K;
  cin >> n >> K;
  poss[0][0] = 1;
  for (int i = 1; i <= n; i++) {
    cin >> a;
    x = 0;
    y = 0;
    while (a % 2 == 0) x++, a >>= 1;
    while (a % 5 == 0) y++, a /= 5;
    memcpy(dp2, dp, sizeof dp);
    memcpy(poss2, poss, sizeof poss);
    for (int j = 0; j < i; j++) {
      int lim = (i - 1) * 25;
      for (int k = 0; k <= lim; k++) {
        if (poss2[j][k]) {
          dp[j + 1][k + y] = max(dp[j + 1][k + y], dp2[j][k] + x);
          poss[j + 1][k + y] = 1;
        }
      }
    }
  }
  int ans = 0;
  for (int i = 0; i <= 25 * n; i++) ans = max(ans, min(i, dp[K][i]));
  cout << ans;
}
