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

N, K = map(int, input().split())
A = list(map(int, input().split()))
mod = pow(10,9)+7

A.sort(reverse=True)

deque = deque()
for a in A:
    deque.append(a)

ans = 1
cnt = 0
if K%2 == 1:
    ans *= deque.popleft()
    cnt += 1
    
if ans <= 0:
    for i in range(K-1):
        ans *= deque.popleft()
        ans %= mod
else:
    while cnt < K:
        x1 = deque.popleft()
        x2 = deque.popleft()
        deque.appendleft(x2)
        deque.appendleft(x1)
        y1 = deque.pop()
        y2 = deque.pop()
        if x1*x2 < y1*y2:
            ans *= y1*y2
            ans %= mod
            cnt += 2
        else:
            ans *= x1*x2
            ans %= mod
            if deque:
                x1 = deque.popleft()
            if deque:
                x2 = deque.popleft()
            deque.append(y2)
            deque.append(y1)
            cnt += 2
            
print(ans)