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

mod = 10 ** 9 + 7
N, K = map(int,input().split())
A = list(map(int,input().split()))
if all([a < 0 for a in A]):
    if K % 2 == 0:
        A.sort()
        ans = 1
        for i in range(K):
            ans *= A[i]
            ans %= mod
        print(ans)
        sys.exit()
    else:
        A.sort(reverse = True)
        ans = 1
        for i in range(K):
            ans *= A[i]
            ans %= mod
        print(ans)
        sys.exit()

A.sort()
l = 0
r = N - 1
ans = 1

if K % 2 == 1:
    ans *= A[r]
    ans %= mod
    r -= 1

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

print(ans)