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
from bisect import bisect_left, bisect_right
n, k = map(int, input().split())
a = list(map(int, input().split()))
a.sort()
na = a[:bisect_left(a, 0)]
pa = a[bisect_right(a, 0):][::-1]
mod = 10**9+7
if k==n:
    ans = 1
    for i in a:
        ans *= i
        ans %= mod
    print(ans)
    exit(0)
if k%2==1 and len(pa)==0:
    ans = 1
    for i in a[::-1][:k]:
        ans *= i
        ans %= mod
    print(ans)
    exit(0)
if k==1:
    print(a[-1])
    exit(0)
if k%2==1:
    rem = pa[-1]
    pa = pa[:-1]
na += [0]*n
pa += [0]*n
nn = 0
pn = 0
ans = 1
for i in range(k//2):
    if i==k//2-1 and k%2==1:
        break
    if pa[pn]*pa[pn+1]>=na[nn]*na[nn+1]:
        ans *= pa[pn]*pa[pn+1]
        pn += 2
    else:
        ans *= na[nn]*na[nn+1]
        nn += 2
    ans %= mod
if k%2==1:
    ans *= max(pa[pn]*pa[pn+1]*max(pa[pn+2], rem), na[nn]*na[nn+1]*max(pa[pn], rem))
print(ans%mod)