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.
import java.util.*;
import java.io.*;
public class Main {
  public static void main(String[] args) throws IOException {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter out = new PrintWriter(System.out);
    StringTokenizer s = new StringTokenizer(br.readLine());
    int n = Integer.parseInt(s.nextToken());
    int k = Integer.parseInt(s.nextToken());
    int [][] num2s5s = new int[n][2]; // contains #2s and #5s for each num
    s = new StringTokenizer(br.readLine());
    for (int i = 0; i < n; i++) {
      long num = Long.parseLong(s.nextToken());
      num2s5s[i][0] = calcNum2s(num);
      num2s5s[i][1] = calcNum5s(num);
    }
    long [][] dp = new long [k+1][26*k+1];
    for (int i = 0; i <=k; i++) {
      for (int j = 0; j <= 26*k; j++) {
        dp[i][j] = -1;
      }
    }
    dp[0][0] = 0;
    for (int i = 0; i < n; i++) {
      int num2s = num2s5s[i][0];
      int num5s = num2s5s[i][1];
      for (int numAdded = Math.min(i+1,k); numAdded >= 1; numAdded--) {
        for (int currNum5s = 26*k; currNum5s >= num5s; currNum5s--) {
          if (dp[numAdded-1][currNum5s-num5s] != -1) {
            dp[numAdded][currNum5s] = Math.max(dp[numAdded][currNum5s],dp[numAdded-1][currNum5s-num5s]+num2s);
          }
        }
      }
    }
    /*for (int i = 0; i <= k; i++) {
      System.out.println(i + " " + Arrays.toString(dp[i]));
    }*/
    long res = 0;
    for (int num5s = 0; num5s <= 26*k; num5s++) {
      res = Math.max(res,Math.min(dp[k][num5s],num5s));
    }
    out.println(res);
    out.close();
  }
  public static int calcNum2s (long num) {
    int res = 0;
    while (num % 2 == 0) {
      num/=2;
      res++;
    }
    return res;
  }
  public static int calcNum5s (long num) {
    int res = 0;
    while (num % 5 == 0) {
      num /= 5;
      res++;
    }
    return res;
  }
}