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 copy import deepcopy
n, k = map(int, input().split())
a = list(map(int, input().split()))
a.sort()
mod = 10 ** 9 + 7
ans = 1
i, j = 0, n - 1
k2 = deepcopy(k)
while k2 > 1:
    if a[i] * a[i + 1] > a[j] * a[j - 1]:
        ans *= a[i] * a[i + 1]
        ans %= mod
        i += 2
        k2 -= 2
    else:
        ans *= a[j]
        j -= 1
        ans %= mod
        k2 -= 1
if k2 == 1:
    ans *= a[j]
    ans %= mod
if a[-1] < 0 and k % 2:
    ans = 1
    for i in range(n - k, n):
        ans *= a[i]
        ans %= mod
print(ans)