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 = 10**9+7
N, K = map(int,input().split())
A = sorted(list(map(int,input().split())))

pi = 1
ni = 0
ans = 1
i = 0
while i < K-1:
  if A[ni]*A[ni+1] > A[-pi]*A[-pi-1]:
    ans = ans*A[ni]*A[ni+1]%mod
    ni += 2
    i += 2
    
  else:
    ans = ans*A[-pi]%mod
    pi += 1
    i += 1
    
if i == K-1:
  ans = ans*A[-pi]%mod
  
if A[-1]<0 and K%2==1:
  ans = 1
  for i in A[N-K:]:
    ans = ans*i%mod

print(ans)
