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

neg_a = sorted([a for a in A if a < 0], reverse=True)
pos_a = sorted([a for a in A if a >= 0])
ans = 1

if len(pos_a) == 0 and K % 2 == 1:
    for a in neg_a[:K]:
        ans = ans * a % MOD
    print(ans)
    exit()

while K > 0:
    if K == 1 or len(neg_a) <= 1:
        if len(pos_a) == 0:
            ans *= neg_a.pop()
        elif len(pos_a) > 0:
            ans *= pos_a.pop()
        K -= 1
    elif len(pos_a) <= 1:
        ans *= neg_a.pop() * neg_a.pop()
        K -= 2
    elif pos_a[-1] * pos_a[-2] > neg_a[-1] * neg_a[-2]:
        ans *= pos_a.pop()
        K -= 1
    else:
        ans *= neg_a.pop() * neg_a.pop()
        K -= 2
    ans %= MOD

print(ans)
