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_i = list(map(int, input().split()))
list.sort(a_i)
ans = 1
isminus = False
if k % 2 == 0:
    left = 0
    right = n - 1
else:
    left = 0
    right = n - 2
    ans *= a_i[n - 1]
if ans < 0: isminus = True
for x in range(k // 2):
    ans_L = a_i[left] * a_i[left + 1]
    ans_R = a_i[right] * a_i[right - 1]
    if (isminus == False and ans_L < ans_R) or (isminus == True and ans_L > ans_R):
        ans *= ans_R
        right -= 2
    else:
        ans *= ans_L
        left += 2
    if ans < 0 or ans >= mod: ans %= mod
print(ans)
