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 = 1000000007

def sgn(v):
    return (v > 0) - (v < 0)

def solve():
    v.sort(key=abs, reverse=True)
    res = 1
    flag = 1
    for i in range(k):
        res *= v[i]
        res %= mod
        flag *= sgn(v[i])
    if flag >= 0:
        return res
    if max(v) <= 0:
        res = 1
        for i in range(-k, 0, 1):
            res *= v[i]
            res %= mod
        return res

    def get(comp):
        i = k - 1
        while i >= 0 and comp(v[i]):
          i -= 1
        j = k
        while j < n and not comp(v[j]):
          j += 1
        if j == n: j = i
        return i, j
      
    i, j = get(lambda w: w >= 0)
    i2, j2 = get(lambda w: w <= 0)
    if i2 >= 0 and v[j] * v[i2] < v[i] * v[j2]:
        i = i2
        j = j2

    res = v[j]
    for a in range(k):
        if a != i:
            res *= v[a]
            res %= mod
    return res

n, k = map(int, input().split(" "))
v = list(map(int, input().split(" ")))
print (solve())