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 = [int(x) for x in input().strip().split(" ")]
p = 10**9 + 7

num_list = [int(x) for x in input().strip().split(" ")]
num_list = sorted(num_list, reverse = True)

ans = 1
l_idx = 0
r_idx = -1

if num_list[0] < 0 and k % 2 == 1:
  for i in range(k):
    ans = (ans * num_list[i]) % p
else:
  while True:
    if k >= 2:
      l_prod = num_list[l_idx] * num_list[l_idx+1]
      r_prod = num_list[r_idx] * num_list[r_idx-1]
      if l_prod >= r_prod:
        ans = (ans * num_list[l_idx]) % p
        l_idx +=1
        k -= 1
      else:
        ans = (ans * r_prod) % p
        r_idx -=2
        k -= 2
    elif k == 1:
      ans = (ans * num_list[l_idx]) % p
      ans %= p
      break
    else:
      break

print(ans)
