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()))
b = []
c = []
d = 1
m = 10**9+7
for i in range(n):
    if a[i] < 0:
        c.append(a[i])
    else:
        b.append(a[i])
b.sort()
c.sort(reverse=True)
if len(b) == 0 and k%2 == 1:
    for i in range(k):
        d = d*c[i]%m
else:
    while k > 0:
        if len(b) > 1 and len(c) > 1:
            if b[-1]*b[-2] < c[-1]*c[-2] and k > 1:
                d = d*c.pop()%m
                d = d*c.pop()%m
                k -= 2
            else:
                d = d*b.pop()%m
                k -= 1
        elif len(b) == 1 and len(c) > 1:
            if k > 1:
                d = d*c.pop()%m
                d = d*c.pop()%m
                k -= 2
            else:
                d = d*b.pop()%m
                k -= 1
        elif len(b) >= 1 and len(c) <= 1:
            d = d*b.pop()%m
            k -= 1
        else:
            d = d*c.pop()%m
            k -= 1
print(d)