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
#

import sys
input=sys.stdin.readline
MOD=10**9+7


def main():
    N,K=map(int,input().split())
    A=list(map(int,input().split()))
    if N==1:
        print(A[0])
        exit()
    A.sort()
    A2n=[]
    for i in range(0,N,2):
        if i+1>=N:
            break
        if A[i]<=0 and A[i+1]<=0:
            A2n.append(A[i]*A[i+1])
        else:
            break

    A.sort(reverse=True)
    ans=1
    if A[0]<=0 and K%2==1:
        for i in range(K):
            ans=(ans*A[i])%MOD
        print(ans)
        exit()
    ni=0
    i=0
    while(K>0):
        if i+1<N and len(A2n)-ni>0 and A[i]*A[i+1]<A2n[ni] and K>=2:
                ans=(ans*A2n[ni])%MOD
                K-=2
                ni+=1
        else:
            ans=(ans*A[i])%MOD
            i+=1
            K-=1
    print(ans)
            
    
    
if __name__=="__main__":
    main()
