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 sys
from decimal import Decimal


def calc(c):
    d = 0
    p = 0
    while c % 2 == 0:
        c /= 2
        d += 1
    while c % 5 == 0:
        c /= 5
        p += 1
    return d, p


def main():
    n, k = map(int, sys.stdin.readline().split())
    a = list(map(int, sys.stdin.readline().split()))
    dp = [[-1] * 5050 for i in range(k+1)]
    for i in range(n):
        d, p = calc(Decimal(a[i]))
        for i in range(k - 2, -1, -1):
            for j in range(5000):
                if dp[i][j] != -1:
                    dp[i + 1][j + p] = max(dp[i + 1][j + p], dp[i][j] + d)
        dp[0][p] = max(dp[0][p], d)


    ans = 0
    for j in range(5050):
        if dp[k-1][j] != -1:
            ans = max(ans, min(j, dp[k-1][j]))

    print(ans)


main()
