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
mod = 10**9 + 7
n, k = map(int, input().split())
a = list(map(int, input().split()))
a.sort()
index_change = 0
ans = 1
for i in range(n-1):
    if a[i] <= 0 and a[i+1] > 0:
        index_change = i+1
        break
else:
    if k % 2 == 1:
        for i in range(1, k+1):
            ans *= a[-i]
            ans %= mod
    else:
        for i in range(k):
            ans *= a[i]
            ans %= mod
    print(ans)
    exit()
l = 0
r = n-1
while k > 0:
    if k == 1:
        if r >= index_change:
            ans *= a[r]
            ans %= mod
            break
        else:
            ans *= a[l]*a[l+1]
            ans %= mod
            ans *= pow(a[r+1], mod-2, mod)
            ans %= mod
            break
    else:
        left = a[l]*a[l+1]
        right = a[r]*a[r-1]
        if left >= right:
            ans *= left
            ans %= mod
            l += 2
            k -= 2
        else:
            ans *= a[r]
            ans %= mod
            r -= 1
            k -= 1
print(ans)