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
if A[-1] >= 0:
    for i in range(K):
        ans *= A[i]
        ans %= MOD
elif A[0] < 0:
    if K % 2 == 0:
        for i in range(K):
            ans *= A[N-1-i]
            ans %= MOD
    else:
        for i in range(K):
            ans *= A[i]
            ans %= MOD
else:
    r,l = N-1,0
    n = 0
    while n < K:
        if K-n == 1:
            ans *= A[l]
            ans %= MOD
            n += 1
        else:
            if A[r]*A[r-1] > A[l]*A[l+1]:
                ans *= (A[r]*A[r-1])
                ans %= MOD
                r -= 2
                n += 2
            else:
                ans *= A[l]
                ans %= MOD
                l += 1
                n += 1
print(ans)
