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
input = sys.stdin.readline
mod = int(1e9+7)
n,k = map(int,input().split())
L=list(map(int,input().split()))

ans = 1
if k==n:
    for i in L:
        ans*=i
        ans%=mod
    print(ans%mod)
    sys.exit()
pos = []
neg = []
for i in L:
    if i>=0:
        pos.append(i)
    else:
        neg.append(i)
pos.sort(reverse=True)
neg.sort()
if len(pos) == 0 and k%2!=0:
    for i in range(1,k+1):
        ans*=neg[-i]
        ans%=mod
    print(ans%mod)
    sys.exit()
if k%2!=0:
    ans*=pos.pop(0)
    k-=1
l=[]
for i in range(1,len(pos),2):
    l.append(pos[i]*pos[i-1])

for i in range(1,len(neg),2):
    l.append(neg[i]*neg[i-1])

l.sort(reverse = True)
for i in range(k//2):
    ans*=l[i]
    ans%=mod

print(ans%mod)
