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
def solve(N, K, A):
    MOD = 10 ** 9 + 7
    ans = 1
    if A[-1] == 0 and K & 1:
        return 0
    if A[-1] < 0 and K & 1:
        for k in range(K):
            ans *= A[~k]
            ans %= MOD
        return ans

    i, j = 0, len(A) - 1
    if K & 1:
        ans *= A[-1]
        j -= 1
    for _ in xrange(K // 2):
        if A[i] * A[i + 1] > A[j] * A[j - 1]:
            ans *= A[i]
            ans %= MOD
            ans *= A[i+1]
            ans %= MOD
            i += 2
        else:
            ans *= A[j]
            ans %= MOD
            ans *= A[j-1]
            ans %= MOD
            j -= 2

    return ans

    

N, K = map(int, raw_input().split())
A = map(int, raw_input().split())
A.sort()
print solve(N, K, A)
