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.
/*
3 2
50 4 20

Smaller case is for every number, what is the largest number of 2s one can get for a certain number of 5s?
*/
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));
    StringTokenizer details = new StringTokenizer(br.readLine());
    int numInts = Integer.parseInt(details.nextToken());
    int setSize = Integer.parseInt(details.nextToken());
    StringTokenizer st = new StringTokenizer(br.readLine());
    int[][] dp = new int[setSize + 1][26 * numInts + 1];
    for(int[] row : dp) Arrays.fill(row, -1);
    for(int x = 0; x < numInts; x++){
      long num = Long.parseLong(st.nextToken());
      int num5 = calc(5, num);
      int num2 = calc(2, num);
      //System.out.println("\n" + num5 + " " + num2);
      dp[0][0] = 0;
      for(int y = Math.min(x + 1, setSize); y >= 1; y--){
        for(int z = numInts * 26; z >= num5; z--){
          //number of 5s
          if(dp[y - 1][z - num5] == -1) continue;
          //System.out.println("works!");
          dp[y][z] = Math.max(dp[y - 1][z - num5] + num2, dp[y][z]);
        }
      }
      //for(int[] row : dp) System.out.println(Arrays.toString(row));
    }
    //for(int[] row : dp) System.out.println(Arrays.toString(row));
    int res = 0;
    for(int x = 0; x <= numInts * 26; x++){
      res = Math.max(res, Math.min(x, dp[setSize][x]));
    }
    System.out.println(res);
    br.close();
  }
  public static int calc(long div, long n){
    int ret = 0;
    while(n%div == 0){
      n /= div;
      ret++;
    }
    return ret;
  }
}