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()
a,b,i=0,1,0
mod=10**9+7
ans=1
while i<K-1:
  if A[a]*A[a+1]>A[-b]*A[-b-1]:
    ans*=A[a]*A[a+1]
    ans%=mod
    a+=2
    i+=2
  else:
    ans*=A[-b]
    ans%=mod
    b+=1
    i+=1
if i==K-1:
  ans*=A[-b]
  ans%=mod
if A[-1]<0 and K%2==1:
  ans=1
  for i in A[N-K:]:
    ans*=i
    ans%=mod
print(ans%mod)