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
mod=1000000007
n,k=map(int, input().split())
lst=list(map(int, input().split()))
lst=sorted(lst)
p=1
if lst[-1]==0 and k%2!=0:
    print(0)
elif lst[-1]<0 and k%2!=0:
    for i in range(n-1,n-k-1,-1):
        #print(p)
        p=(p%mod*lst[i]%mod)%mod
    #print(p)
    print(p%mod)
else:
    j=n-1
    if k%2!=0:
        p*=lst[j]
        k-=1
        j-=1
    k=k//2
    i=0
    for x in range(k):
        if lst[i]*lst[i+1]>lst[j]*lst[j-1]:
            p=(p%mod*lst[i]%mod*lst[i+1]%mod)%mod
            i+=2
        else:
            p=(p%mod*lst[j]%mod*lst[j-1]%mod)%mod
            j-=2
    #print(p)
    print(p%mod)