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 = 10**9 + 7
A.sort(reverse=True)

ans = 1
B = deque(A)

if K % 2 == 1:
    ans *= B.popleft()

for _ in range(K // 2):
    l = B[0] * B[1]
    r = B[-1] * B[-2]
    if l >= r:
        ans *= B.popleft() * B.popleft()
    else:
        ans *= B.pop() * B.pop()
    if ans > 0: ans %= MOD
    else: ans = (ans % MOD) - MOD

if ans < 0:
    ans = 1
    for a in A[:K]:
        ans *= a
        ans %= MOD

print(ans % MOD)
