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())
arr=list(map(int,input().split()))
arr.sort(reverse=True)
n=len(arr)
l=0
r=n-1
ans=1
if k%2==1:
    ans=arr[0]
    l=1
m=10**9+7
if ans<0:
    ans=1
    for i in range(k):
        ans*=arr[i]
        ans%=m
    print(ans)
    quit()
for i in range(k//2):
    po=arr[l]*arr[l+1]
    ne=arr[r]*arr[r-1]
    if po>=ne:
        l+=2
        ans*=po
        ans%=m
    else:
        r-=2
        ans*=ne
        ans%=m
print(ans)

