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()))
mod = 10**9 + 7
res = 1
a.sort(reverse=True)
if a[0]<0 and k%2==1:
    for i in range(k):
        res = (res*a[i])%mod
else:
    right = n-1
    left = 0
    while k > 1:
        if a[right]*a[right-1] < a[left]*a[left+1]:
            res = (res*a[left])%mod
            left += 1
            k -= 1
        else:
            res = (res*a[right]*a[right-1])%mod
            right -= 2
            k -= 2
    if k == 1:
        res = (res*a[left])%mod

print(res)