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_neg = []
A_pos = []
 
for i in range(N):
  if A[i] <= 0:
    A_neg.append(-A[i])
  else:
    A_pos.append(A[i])
 
A_neg.sort(reverse=True)
A_pos.sort(reverse=True)
 
ans = 1
 
if K == N:
  for i in range(N):
    ans *= (A[i]%1000000007)
    ans %= 1000000007
  print(ans)
 
elif K%2==1 and len(A_pos)==0:
  for i in range(1, K+1):
    ans *= ((-A_neg[-i])%1000000007)
    ans %= 1000000007
  print(ans)
 
else:
  if K%2==1:
    ans *= A_pos.pop(0)
    K -= 1
  buf = []
  for i in range(len(A_pos)//2):
    buf.append(A_pos[2*i]*A_pos[2*i+1])
  for i in range(len(A_neg)//2):
    buf.append(A_neg[2*i]*A_neg[2*i+1])
  buf.sort(reverse=True)
  for i in range(K//2):
    ans *= (buf[i]%1000000007)
    ans %= 1000000007
  print(ans)
  
