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
# coding: utf-8
N,K=map(int,input().split())
A=list(map(int,input().split()))
MOD=10**9+7

ans=1

if K==N:
    for i in range(N):
        ans*=A[i]
        if ans>0:
            ans=ans%MOD
elif max(A)<=0 and K%2==1:
    A.sort(reverse=True)
    for i in range(K):
        ans*=A[i]
        if ans>0:
            ans=ans%MOD
else:
    Ap=[]
    Am=[]
    
    for i in range(N):
        if A[i]>0:
            Ap.append(A[i])
        else:
            Am.append(A[i])
        

    Ap.sort(reverse=True)
    Am.sort()
    
    if K%2==1 and Ap:
        ans*=Ap.pop(0)
    
    P=[]
    
    for i in range(len(Ap)//2):
        P.append(Ap[i*2]*Ap[i*2+1])
    
    for i in range(len(Am)//2):
        P.append(Am[i*2]*Am[i*2+1])
    
    P.sort(reverse=True)
    
    for i in range(K//2):
        ans*=P[i]
        ans=ans%MOD

print(ans%MOD)