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=sorted(list(map(int,input().split())))

mod=10**9+7

if A[-1]<0 and k%2==1:
    now=1
    for i in range(k):
        now*=A[-i-1]%mod
        now%=mod
    print(now)
    exit()

l=0
r=n-1
ans=1
if k%2==1:
    ans=A[-1]
    r-=1

for i in range(k//2):
    mi=A[l]*A[l+1]
    pl=A[r]*A[r-1]
    if mi>pl:
        ans*= mi%mod
        ans%=mod
        l+=2
    else:
        ans*= pl%mod
        ans%=mod
        r-=2
print(ans%mod)