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=sorted(a,reverse=True)
mod=10**9+7
l=0
r=n-1
ans=1
if k%2==1:
  ans=a[0]
  l=1
if ans<0:
  c=1
  for i in range(k):
    c=c*a[i]%mod
  print(c)
  
else:
  for i in range(k//2):
    L=a[l]*a[l+1]
    R=a[r]*a[r-1]
    if L>=R:
      ans=ans*L%mod
      l+=2
    else:
      ans=ans*R%mod
      r-=2
  print(ans)
      