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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class cf837d {
    public static int A = 300;
    public static int B = 300 * 30;
    private static int[][] dp = new int[A][B];
    private static int[] cnt2 = new int[205];
    private static int[] cnt5 = new int[205];

    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()); //elements
        int K = Integer.parseInt(st.nextToken()); //subset size
        st = new StringTokenizer(br.readLine());

        //Find freq of twos and fives.
        for (int i = 0; i < N; i++) {
            long value = Long.parseLong(st.nextToken());
            while (value % 2 == 0) {
                value /= 2;
                cnt2[i]++;
            }
            while (value % 5 == 0) {
                value /= 5;
                cnt5[i]++;
            }
        }
        //System.out.println("CNT2: " + Arrays.toString(cnt2));
        //System.out.println("CNT5: " + Arrays.toString(cnt5));

        //Initialize
        int ans = 0;
        for (int i = 0; i < A; i++) {
            Arrays.fill(dp[i], -1);
        }

        dp[0][0] = 0;
        dp[1][cnt5[0]] = cnt2[0];
        for (int i = 1; i < N; i++) {
            for (int j = K - 1; j >= 0; j--) {
                for (int pos = B - 1; pos >= 0; pos--) {
                    if ((pos + cnt5[i] < B) && (dp[j][pos] >= 0)) {
                        dp[j + 1][pos + cnt5[i]] = Integer.max((dp[j + 1][pos + cnt5[i]]), (dp[j][pos] + cnt2[i]));
                    }
                }
            }
        }

        for (int i = 0; i < B; i++) {
            if (dp[K][i] >= 0) {
                int temp = Math.min(i, dp[K][i]);
                ans = Integer.max(ans, temp);
            }
        }
        System.out.println(ans);


    }
}
