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.sort()
div=7+10**9
ans=1
t=0
i,j=0,N-1

if A[-1]<0 and K%2==1:
    for i1 in range(N-K,N):
        ans*=A[i1]
        ans%=div
else:
    while t<K-1:
        if A[i]*A[i+1]>A[j]*A[j-1]:
            ans*=A[i]*A[i+1]
            ans%=div
            i+=2
            t+=2
        else:
            ans*=A[j]
            ans%=div
            j+=-1
            t+=1
    if t==K-1:
        ans*=A[j]
        ans%=div

print(ans)