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 inf = 210;
const int max_n = 210;
const int max_size2 = 205 * 64;
const int max_size5 = 205 * 35;
short int c_5[max_n], c_2[max_n];
short int dp[max_size2][max_size5];
int main() {
  int n, t;
  cin >> n >> t;
  int sum2 = 0;
  int sum5 = 0;
  for (int i = 0; i < n; i++) {
    long long a;
    cin >> a;
    long long tmp = a;
    while (tmp % 2 == 0) c_2[i]++, tmp /= 2;
    tmp = a;
    while (tmp % 5 == 0) c_5[i]++, tmp /= 5;
  }
  for (int i = 0; i < max_size2; i++)
    for (int j = 0; j < max_size5; j++) dp[i][j] = inf;
  dp[0][0] = 0;
  int ans = 0;
  for (int i = 0; i < n; i++) {
    sum2 += c_2[i];
    sum5 += c_5[i];
    for (int j = sum2; j >= c_2[i]; j--)
      for (int k = sum5; k >= c_5[i]; k--) {
        dp[j][k] = min(dp[j][k], (short int)(dp[j - c_2[i]][k - c_5[i]] + 1));
        if (dp[j][k] <= t) ans = max(ans, min(j, k));
      }
  }
  cout << ans << endl;
  return 0;
}
