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 = (int(x) for x in input().split())
A = list(int(x) for x in input().split())
MOD = 10**9 + 7
A.sort()

l = 0
r = n - 1
flag = False  # マイナスになってしまうかフラグ
ans = 1
if k % 2 == 1:
    ans = A[r]
    r -= 1
    k -= 1
    if ans < 0:
        flag = True


if flag:  # どうしてもマイナスになってしまう場合(kが奇数で要素すべてがマイナスの場合)
    while k:
        ans *= A[r] * A[r - 1] % MOD
        ans %= MOD
        r -= 2
        k -= 2
else:  # 必ず0以上にできる場合
    while k:
        x = A[l] * A[l + 1]
        y = A[r] * A[r - 1]
        if x > y:
            ans *= x % MOD
            ans %= MOD
            l += 2
        else:
            ans *= y % MOD
            ans %= MOD
            r -= 2
        k -= 2

print(ans)
