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
import sys

sys.setrecursionlimit(500005)
stdin = sys.stdin

ni = lambda: int(ns())
na = lambda: list(map(int, stdin.readline().split()))
ns = lambda: stdin.readline().strip()

n, k = na()
a = na()

neg = []
pos = []
for i in range(n):
    if a[i] < 0:
        neg.append(a[i])
    elif a[i] > 0:
        pos.append(a[i])
neg.sort()
pos.sort(reverse=True)

mx = -1
arg = -1
lall = 0

nn, np = 0, k
while np > len(pos):
    np -= 2
    nn += 2

if np >= 0 and nn <= len(neg):
    arg = nn
    while np-2 >= 0 and nn+1 < len(neg):
        if pos[np-1] * pos[np-2] < neg[nn] * neg[nn+1]:
            nn += 2
            np -= 2
            arg = nn
        else:
            break

ans = 1
mod = 1000000007
if arg == -1:
    a.sort(reverse=True)
    for i in range(k):
        ans = ans * a[i] % mod
    print(ans)
else:
    for i in range(arg):
        ans = ans * neg[i] % mod
    for i in range(k-arg):
        ans = ans * pos[i] % mod
    print(ans)
