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 maxn = 1e6 + 10;
const int MOD = 1e9 + 7;
int dp[210][5200];
int e2[210], e5[210];
int main() {
  int n, k;
  cin >> n >> k;
  for (int i = 1; i <= n; ++i) {
    long long e;
    cin >> e;
    for (long long x = e; x % 2 == 0 and x > 0; x /= 2) e2[i]++;
    for (long long x = e; x % 5 == 0 and x > 0; x /= 5) e5[i]++;
  }
  for (int i = 0; i < 210; ++i) fill(dp[i], dp[i] + 5200, -1e9);
  dp[0][0] = 0;
  int max_e5 = 0;
  for (int i = 1; i <= n; ++i) {
    max_e5 += e5[i];
    for (int j = i; j >= 1; --j) {
      for (int ex5 = max_e5; ex5 >= e5[i]; --ex5) {
        dp[j][ex5] = max(dp[j - 1][ex5 - e5[i]] + e2[i], dp[j][ex5]);
      }
    }
  }
  int ans = 0;
  for (int ex5 = 0; ex5 <= max_e5; ++ex5) {
    ans = max(min(dp[k][ex5], ex5), ans);
  }
  cout << ans << endl;
  return 0;
}
