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
#/usr/bin/python

def solve():
    n, k = map(int, input().split())
    a = sorted(map(int, input().split()), reverse=True)

    mod = 10 ** 9 + 7
    l = 0
    r = n - 1
    ans = 1

    if k % 2 == 1:
        ans = a[0]
        l = 1

    # If the maximum number is negative and k is odd, the answer is the product of the first k numbers.
    if ans < 0:
        mul = 1
        for i in range(k):
            mul = mul * a[i] % mod
        return mul

    # otherwise, multiply the leftmost two products and the rightmost two products, whichever is larger.
    for i in range(k//2):
        l_mul = a[l] * a[l+1]
        r_mul = a[r] * a[r-1]
        if l_mul >= r_mul:
            ans = ans * l_mul % mod
            l += 2
        else:
            ans = ans * r_mul % mod
            r -= 2

    return ans

print(solve())
