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

ans=1
mod=10**9+7

a.sort()
if a[0]>=0:
    for i in range(n-1,n-k-1,-1):
        ans*=a[i]
        ans%=mod
    print(ans)
    exit()
if a[-1]<=0:
    if k%2:
        for i in range(n-1,n-k-1,-1):
            ans*=a[i]
            ans%=mod
    else:
        for i in range(k):
            ans*=a[i]
            ans%=mod
    print(ans)
    exit()
l=0;r=n-1
if k%2:
    ans=a[-1]
    r-=1
    k-=1
while k:
    if a[l]*a[l+1]>a[r]*a[r-1]:
        ans*=a[l]*a[l+1]
        l+=2
    else:
        ans*=a[r]*a[r-1]
        r-=2
    k-=2
    ans%=mod
   
print(ans)
    
    

