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
"""
E.
"""
from functools import reduce
from collections import deque


def prod(x, y):
    return x * y % MOD

    
N, K = map(int, input().split())
a_list = list(map(int, input().split()))
a_list.sort(reverse=True)
# abs_a_list = sorted(a_list, key=abs, reverse=True)
MOD = 10**9 + 7

if K%2 == 1:
    flg = True
    for a in a_list:
        if a >= 0:
            flg = False
            break
    if flg:
        print(reduce(prod, a_list[:K]))
        exit()

S = []
a_list = deque(a_list)
i = 0
while i < K:
    if len(a_list)>=2:
        if a_list[0]*a_list[1] > a_list[-1]*a_list[-2]:
            S.append(a_list.popleft())
            i += 1
        elif a_list[0]*a_list[1] <= a_list[-1]*a_list[-2] and i <= K-2:
            S.append(a_list.pop())
            S.append(a_list.pop())
            i += 2
        else:
            S.append(a_list.popleft())
            i += 1
    else:
        S.append(a_list.popleft())
        i += 1
        
ans = reduce(prod, S)
print(ans)