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 long long N = 210;
long long dp[N * 26][N];
signed main() {
  memset(dp, 0x80, sizeof dp);
  dp[0][0] = 0;
  long long n, K;
  cin >> n >> K;
  long long t5 = 0;
  for (long long i = 1; i <= n; i++) {
    long long p2 = 0, p5 = 0, x;
    cin >> x;
    while (x % 2 == 0) {
      x /= 2;
      p2++;
    }
    while (x % 5 == 0) {
      x /= 5;
      p5++;
    }
    t5 += p5;
    for (long long k = min(i, K); k >= 1; k--)
      for (long long j = t5; j >= p5; j--) {
        dp[j][k] = max(dp[j][k], dp[j - p5][k - 1] + p2);
      }
  }
  long long ans = 0;
  for (long long i = 0; i <= t5; i++) ans = max(ans, min(i, dp[i][K]));
  cout << ans << "\n";
}
