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
import sys
from collections import deque

read = sys.stdin.read
readline = sys.stdin.readline
readlines = sys.stdin.readlines
sys.setrecursionlimit(10 ** 9)
INF = 1 << 60
MOD = 1000000007


def main():
    N, K, *A = map(int, read().split())

    pos = [a for a in A if a >= 0]
    neg = [a for a in A if a < 0]

    pos.sort()
    neg.sort(reverse=True)

    if N == K:
        vec = A
    elif N == len(neg):
        if K & 1:
            vec = neg[:K]
        else:
            vec = neg[-K:]
    else:
        vec = []
        if K & 1:
            vec.append(pos.pop())

        tmp = []
        while len(neg) >= 2:
            tmp.append(neg.pop() * neg.pop())
        while len(pos) >= 2:
            tmp.append(pos.pop() * pos.pop())

        tmp.sort(reverse=True)
        vec.extend(tmp[: K // 2])

    ans = 1
    for a in vec:
        ans = ans * a % MOD

    print(ans)
    return


if __name__ == '__main__':
    main()
