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

A.sort()

ans = 1
mod = 10 ** 9 + 7

if 0 <= A[0]:
    for i in range(N - 1, N - K - 1, -1):
        ans = (ans * A[i]) % mod
elif A[-1] <= 0:
    if K % 2:
        for i in range(N - 1, N - K - 1, -1):
            ans = (ans * A[i]) % mod
    else:
        for i in range(K):
            ans = (ans * A[i]) % mod
else:
    l = 0
    r = N - 1
    if K % 2:
        ans = A[-1]
        r -= 1
        K -= 1

    while K:
        if A[l] * A[l + 1] < A[r] * A[r - 1]:
            ans = (ans * A[r] * A[r - 1]) % mod
            r -= 2
        else:
            ans = (ans * A[l] * A[l + 1]) % mod
            l += 2
        K -= 2

print(ans)
