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
n, k = map(int, input().split())

a = list(map(int, input().split()))
a_pos = sorted([i for i in a if i >= 0])
a_neg = sorted([i for i in a if i < 0], reverse=True)

mod = 10 ** 9 + 7
ans = 1

if len(a_pos) == 0 and k % 2:
    for i in a_neg[:k]:
        ans = ans * i % mod
    print(ans)
    exit()

while k > 0:
    if k == 1 or len(a_neg) <= 1:
        if len(a_pos) == 0:
            ans *= a_neg.pop()
        elif len(a_pos) > 0:
            ans *= a_pos.pop()
        k -= 1
    elif len(a_pos) <= 1:
        ans *= a_neg.pop() * a_neg.pop()
        k -= 2
    
    elif a_pos[-1] * a_pos[-2] > a_neg[-1] * a_neg[-2]:
        ans *= a_pos.pop()
        k -= 1
    elif a_pos[0] * a_pos[1] <= a_neg[-1] * a_neg[-2]:
        ans *= a_neg.pop() * a_neg.pop()
        k -= 2
    ans %= mod

else:
    print(ans)