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(key=abs, reverse=True)
s = 0
ps = 0
for i in range(k):
    if a[i] < 0:
        s ^= 1
    else:
        ps = 1
b = a[:k]
b.sort(key=abs)
if s:
    p = -MOD
    for i in range(k, n):
        if a[i] >= 0:
            p = a[i]
            break
    q = MOD
    if ps:
        for i in range(k, n):
            if a[i] <= 0:
                q = a[i]
                break
    x = 0
    for j in range(k):
        if b[j] < 0:
            x = b[j]
            xi = j
            break
    y = 0
    for j in range(k):
        if b[j] > 0:
            y = b[j]
            yi = j
            break
    flg = 1
    if y == 0:
        if p >= 0:
            b[xi] = p
            flg = 0
    else:
        if p * y > q * x and p > 0:
            b[xi] = p
        elif q < 0:
            b[yi] = q
        flg = 0
    if flg:
        b = a[-k:]
res = 1
for i in range(k):
    res = res * b[i] % MOD
print(res)
