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

input = sys.stdin.readline

n_k = list(map(int, input().split()))
n = n_k[0]
k = n_k[1]
a = list(map(int, input().split()))
a_pos = list(filter(lambda v: v >= 0, a))
a_neg = list(filter(lambda v: v < 0, a))

a_pos.sort(reverse=True)
a_neg.sort()

mod = 10**9+7

ans = 1
if n == k:
    for a_i in a:
        ans = ans * a_i % mod
elif len(a_pos) == 0 and k % 2 == 1:
    for i in reversed(range(len(a_neg) - k, len(a_neg))):
        ans = ans * a_neg[i] % mod
else:
    i_p = 0
    i_n = 0
    i = 0
    while i < k:
        if i_p < len(a_pos) and (i == k - 1 or i_n+1 >= len(a_neg) or a_pos[i_p] * (a_pos[i_p+1] if i_p+1 < len(a_pos) else 1) > a_neg[i_n] * a_neg[i_n+1]):
            ans = ans * a_pos[i_p] % mod
            i_p += 1
            i += 1
        else:
            ans = ans * a_neg[i_n] % mod * a_neg[i_n+1] % mod
            i_n += 2
            i += 2
print(ans)
