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
readline = sys.stdin.buffer.readline
read = sys.stdin.read
from collections import deque
sys.setrecursionlimit(10 ** 8)
INF = float('inf')
MOD = 10 ** 9 + 7

def main():
    n, k = map(int, readline().split())
    A = list(map(int, readline().split()))
    MOD = int(1e9) + 7
    A.sort()
    ans = 1
    if A[n - 1] == 0 and (k & 1):
        ans = 0
    elif A[n - 1] <= 0 and (k & 1):
        for i in range(n - 1, n - k - 1, -1):
            ans = (ans * A[i]) % MOD
    else:
        i = 0
        j = n - 1
        if k & 1:
            ans = (ans * A[j]) % MOD
            j -= 1
            k -= 1
        k >>= 1
        for itr in range(k):
            left_product = A[i] * A[i + 1]
            right_product = A[j] * A[j - 1]
            if left_product > right_product:
                ans = (ans * left_product) % MOD
                i += 2
            else:
                ans = (ans * right_product) % MOD
                j -= 2

    print(ans % MOD)

if __name__ == '__main__':
    main()