Given are N integers A_1,\ldots,A_N.

We will choose exactly K of these elements. Find the maximum possible product of the chosen elements.

Then, print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Constraints

* 1 \leq K \leq N \leq 2\times 10^5
* |A_i| \leq 10^9

Input

Input is given from Standard Input in the following format:


N K
A_1 \ldots A_N


Output

Print the maximum product modulo (10^9+7), using an integer between 0 and 10^9+6 (inclusive).

Examples

Input

4 2
1 2 -3 -4


Output

12


Input

4 3
-1 -2 -3 -4


Output

1000000001


Input

2 1
-1 1000000000


Output

1000000000


Input

10 10
1000000000 100000000 10000000 1000000 100000 10000 1000 100 10 1


Output

999983200
mod = 10**9+7

N, K = map(int, input().split())
A = list(map(int, input().split()))

A.sort(reverse=True)

ans = 1
left = 0
right = len(A)-1

# 全部負のとき
if A[0] < 0 and K % 2 == 1:
    for i in range(K):
        ans = (ans * A[i]) % mod
elif K % 2 == 0:
    while K > 0:
        r = A[right] * A[right-1]
        l = A[left] * A[left + 1]
        if l > r:
            ans = (ans * l) % mod
            left += 2
        else:
            ans = (ans * r) % mod
            right -= 2
        K -= 2
else:
    p = A.pop(0)
    K -= 1
    right -= 1
    while K > 0:
        r = A[right] * A[right-1]
        l = A[left] * A[left + 1]
        if l > r:
            ans = (ans * l) % mod
            left += 2
        else:
            ans = (ans * r) % mod
            right -= 2
        K -= 2
    ans = (ans * p) % mod
while ans < 0:
    ans = ans + mod

print(ans)
