837_D. Round Subset
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.
```python
import sys

n, K = map(int, input().split())
a = list(map(int, input().split()))
m2, m5 = [0]*n, [0]*n

for i, x in enumerate(a):
    while x % 2 == 0:
        x //= 2
        m2[i] += 1

    while x % 5 == 0:
        x //= 5
        m5[i] += 1

dp = [[-10**9]*5100 for _ in range(K)]
dp[0][0] = 0

for i in range(n):
    x, y = m5[i], m2[i]
    for j in range(min(K-1, i)-1, -1, -1):
        for k in range(5000, -1, -1):
            dp[j+1][k+x] = max(dp[j+1][k+x], dp[j][k] + y)

    dp[0][x] = max(dp[0][x], y)

ans = 0
for i in range(5001):
    ans = max(ans, min(i, dp[-1][i]))

print(ans)

```