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=[0]*n
a=list(map(int,input().split()))
a=sorted(a)
mod=10**9+7
ans=1

if (k%2==0 or a[-1]>=0):
    mlt1=a[0]*a[1]
    mlt2=a[-2]*a[-1]
    l=0
    r=-1
    for i in range(k//2):
        if (mlt1>=mlt2):
            ans*=mlt1%mod
            l+=2
            if (l<=n-2):
                mlt1=a[l+1]*a[l]
        else:
            ans*=mlt2%mod
            r-=2
            if (r>=-n+1):
                mlt2=a[r-1]*a[r]
        ans%=mod
    if (k%2==1):
        ans*=a[r]
        ans%=mod
    
else:
    for i in range(k):
        ans*=a[n-1-i]
        ans%=mod
        
print(ans)