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

N, K = map(int, input().split())
A = list(map(int, input().split()))
MOD = 10**9+7
p, n = [], []

for i in range(N):
    if A[i]>=0:
        p.append(A[i])
    else:
        n.append(A[i])

ok = False

if len(p)>0:
    if N==K:
        if len(n)%2==0:
            ok = True
    else:
        ok = True
else:
    if K%2==0:
        ok = True

if not ok:
    A.sort(key=lambda x: abs(x))
    ans = 1
    
    for Ai in A[:K]:
        ans *= Ai
        ans %= MOD

    print(ans)
    exit()

p.sort(reverse=True)
n.sort()

if K%2==1:
    ans = p[0]
    p = p[1:]
else:
    ans = 1
    
l = []
    
for i in range(len(p)//2):
    l.append(p[2*i]*p[2*i+1])
    
for i in range(len(n)//2):
    l.append(n[2*i]*n[2*i+1])

l.sort(key=lambda x: abs(x), reverse=True)

for li in l[:K//2]:
    ans *= li
    ans %= MOD
    
print(ans)
