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
from bisect import bisect

N,K = map(int,input().split())
Ali = list(map(int,input().split()))
ans = 1
Ali.sort()
mod = 10**9+7

if K%2 == 1:
  ans = Ali.pop()
  K -= 1
  
Am = Ali[0:bisect(Ali,0)]
Ap = Ali[bisect(Ali,0):]

if ans>=0:
  Am.sort(reverse = True)
  Ap.sort()
else:
  Am.sort()
  Ap.sort(reverse = True)

mp = len(Am)-1
pp = len(Ap)-1

while K>0:
  mmax = -1
  pmax = -1
  if mp >= 1:
    mmax = Am[mp]*Am[mp-1]
  if pp >= 1:
    pmax = Ap[pp]*Ap[pp-1]
    
  if mmax == pmax == -1:
    ans *= Am[0]*Ap[0]
    print(ans%mod)
    exit()
    
  if mmax >= pmax:
    ans = ans * mmax % mod
    mp -= 2
    K -= 2
  else:
    ans = ans * pmax % mod
    pp -= 2
    K -= 2
  



print(ans%mod)