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()
mod=10**9+7
ans=1

if K%2==1 and A[-1]<0:
    for i in range(K):
        ans=ans*A[N-(i+1)]%mod
    print(ans)
    exit()

l=0
r=N-1
if K%2==1:
    ans=ans*A[r]
    r-=1

for _ in range(K//2):
    ml=A[l]*A[l+1]
    mr=A[r]*A[r-1]
    if ml>mr:
        ans=ans*ml%mod
        l+=2
    else:
        ans=ans*mr%mod
        r-=2

print(ans)
