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.awt.*;
import java.util.Arrays;
import java.util.Scanner;

public class RoundSubset {
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int n = scan.nextInt();
        int k = scan.nextInt();
        long[] array = new long[n];
        for (int i = 0; i < n; i++)
            array[i] = scan.nextLong();

        Point[] power_2_5 = new Point[n];
        for (int i = 0; i < n; i++)
            power_2_5[i] = new Point(0, 0);

        int sumPow_2 = 0;
        for (int i = 0; i < n; i++) {
            long temp = array[i];
            while (temp % 2 == 0) {
                power_2_5[i].x++;
                temp /= 2;
            }
            temp = array[i];
            while (temp % 5 == 0) {
                power_2_5[i].y++;
                temp /= 5;
            }

            sumPow_2 += power_2_5[i].x;
        }

        int[][] dp = new int[sumPow_2 + 1][k + 1];
        for (int[] x : dp)
            Arrays.fill(x, -1);
        dp[0][0] = 0;

        for (int i = 0; i < n; i++)
            for (int j = sumPow_2; j >= power_2_5[i].x; j--)
                for (int z = k; z > 0; z--)
                    if (dp[j - power_2_5[i].x][z - 1] >= 0)
                        dp[j][z] = Math.max(dp[j][z], dp[j - power_2_5[i].x][z - 1] + power_2_5[i].y);

        int ans = 0;
        for (int i = 0; i <= sumPow_2; i++)
            ans = Math.max(ans, Math.min(i, dp[i][k]));

        System.out.println(ans);

        scan.close();
    }

}