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 collections import deque

div = 10 ** 9 + 7

n, k = map(int, input().split())
A = deque(sorted([int(x) for x in input().split()]))
maxA = A[-1]
ans = 1
for i in range(k // 2):
    l1 = A[0]
    l2 = A[1]
    r1 = A[-1]
    r2 = A[-2]
    l = l1 * l2
    r = r1 * r2
    if k % 2 == 1 and maxA < 0:
        ans *= r
        ans %= div
        A.pop()
        A.pop()
    else:
        if l < r:
            ans *= r
            ans %= div
            A.pop()
            A.pop()
        else:
            ans *= l
            ans %= div
            A.popleft()
            A.popleft()
if k % 2 == 1:
    ans *= A[-1]
    ans %= div
print(ans)
