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()))

s = sorted(a,reverse=True)
mod = 10**9 + 7
ans = 1

if k % 2 == 1 and s[0] < 0:
        for i in range(k):
            ans = ans * s[i] % mod
        print(ans)
        exit()

l = 0
r = n - 1
if k % 2 == 1:
  ans = ans * s[l]
  l += 1

for _ in range(k // 2):
  ml = s[l] * s[l + 1]
  mr = s[r] * s[r - 1]
  if ml > mr:
    ans = ans * ml % mod
    l += 2
  else:
    ans = ans * mr % mod
    r -= 2

print(ans)