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()))
m,p,z=[],[],0
for a in A:
    if a<0:
        m.append(a)
    elif a>0:
        p.append(a)
    else:
        z+=1
m.sort()
p.sort()
mod=10**9+7
from functools import reduce
if (len(p) or K%2==0) and K<len(m)+len(p) or K==len(m)+len(p) and len(m)%2==0:
    r=1
    i,j=0,0
    while i+j<K:
        if i<len(m)-1 and i+j<K-1 and (j>=len(p)-1 or m[i]*m[i+1]>p[-j-1]*p[-j-2]):
            r=r*m[i]*m[i+1]%mod
            i+=2
        else:
            r=r*p[-j-1]%mod
            j+=1
    print(r)
elif z:
    print(0)
else:
    print(reduce(lambda x,y:x*y%mod,(m+p)[-K:]))