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()))
mod = 10 ** 9 + 7

plus = []
minus = []
for i in a:
    if i >= 0: plus.append(i)
    if i < 0: minus.append(-i)
plus.sort(reverse=True)
minus.sort(reverse=True)

ans = 1
i, j = 0, 0
if n == k:
    if len(plus) % 2 == 1:
        ans *= plus[0]
        i += 1
    if len(minus) % 2 == 1:
        ans *= -minus[0]
        j += 1
if n != k and k % 2 == 1:
    if len(plus) != 0:
        ans = plus[0]
        i += 1
    else:
        minus.sort()
        ans = -minus[0]
        j += 1
while i + j != k:
    x_p = plus[i] * plus[i + 1] if i < len(plus) - 1 else 0
    x_m = minus[j] * minus[j + 1] if j < len(minus) - 1 else 0
    if x_p >= x_m and i != len(plus):
        ans = (ans * x_p) % mod
        i += 2
    else:
        ans = (ans * x_m) % mod
        j += 2
print(ans)
