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()))

#n=10000
#k=n//2
#a=[100000000*(-1)**i for i in range(n)]

mod=pow(10,9)+7
a.sort()
if a[-1]<=0:
  if k%2==0:
    ans=1
    for i in range(k):
      ans*=a[i]
      ans%=mod
    print(ans%mod)
  else:
    ans=1
    for i in range(k):
      ans*=a[-1-i]
      ans%=mod
    print(ans%mod)
elif a[0]>=0:
  ans=1
  for i in range(k):
    ans*=a[-1-i]
    ans%=mod
  print(ans%mod)
else:
  from collections import deque
  a=deque(a)
  ans=1
  while k:
    if k==1:
      ans*=a.pop()
      ans%=mod
      k-=1
    else:
      if a[0]*a[1]>=a[-1]*a[-2]:
        ans*=a.popleft()
        ans*=a.popleft()
        ans%=mod
        k-=2
      else:
        ans*=a.pop()
        ans*=a.pop()
        ans%=mod
        k-=2
  print(ans)
        