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
# coding: utf-8
from functools import reduce


def solve(*args: str) -> str:
    n, k = map(int, args[0].split())
    A = sorted(map(int, args[1].split()))
    mod = 10**9+7

    if n == k:
        return str(reduce(lambda a, b: (a*b) % mod, A, 1))

    if k % 2 and A[-1] < 0:
        return str(reduce(lambda a, b: (a*b) % mod, A[n-k:], 1))

    l, r = 0, n-1
    count = 0
    ret = 1

    if k % 2:
        ret *= A[-1]
        r -= 1
        count += 1

    while count < k-1:
        pos = max(0, A[r]*A[r-1])
        neg = max(0, A[l]*A[l+1])
        if pos <= neg:
            ret *= neg
            l += 2
        else:
            ret *= pos
            r -= 2
        ret %= mod
        count += 2

    return str(ret % mod)


if __name__ == "__main__":
    print(solve(*(open(0).read().splitlines())))
