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
from functools import reduce

mod = 10 ** 9 + 7

N, K, *A = map(int, open(0).read().split())

A.sort(reverse=True)

ans = 1
l, r = 0, N - 1
if K % 2 == 1:
    ans = A[0]
    l = 1

if ans < 0:
    print(reduce(lambda a, b: a * b % mod, A[:K], 1))
    quit()


for i in range(K // 2):
    L = A[l] * A[l + 1]
    R = A[r] * A[r - 1]
    if L >= R:
        ans *= L
        l += 2
    else:
        ans *= R
        r -= 2
    ans %= mod

print(ans)