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 cf837dv2 {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        int N = Integer.parseInt(st.nextToken());
        int K = Integer.parseInt(st.nextToken());
        int[][] num2s5s = new int[N][2]; //@todo  contains #2s and #5s for each num
        st = new StringTokenizer(br.readLine());
        for (int i = 0; i < N; i++) {
            long num = Long.parseLong(st.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);
                    }
                }
            }
        }
        long res = 0;
        for (int num5s = 0; num5s <= 26 * K; num5s++) {
            res = Math.max(res, Math.min(dp[K][num5s], num5s));
        }
        System.out.println(res);
    }

    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;
    }
}
