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()))
MOD = 10 ** 9 + 7

X = sorted([a for a in A if a >= 0])
Y = sorted([a for a in A if a < 0], key=lambda x: abs(x))
ans = 1

if 2 * (min(K, len(Y)) // 2) + len(X) >= K:
    if K % 2 == 1:
        ans *= X.pop()
        K -= 1

    XX = [(x1 * x2) for x1, x2 in zip(*[iter(X[::-1])] * 2)]
    YY = [(y1 * y2) for y1, y2 in zip(*[iter(Y[::-1])] * 2)]
    ZZ = sorted(XX + YY)

    for i in range(K // 2):
        ans *= ZZ.pop()
        ans %= MOD

else:
    Z = sorted(X + Y, key=lambda x: abs(x), reverse=True)
    for i in range(K):
        ans *= Z.pop()
        ans %= MOD

print(ans)
