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
def solve(n,k,a):
    mod = 10**9 + 7
    ans = 1
    l = 0
    r = n-1
    a.sort()
    
    if k%2 == 1:
        ans *= a[r]
        r-=1
    
    if ans < 0:
        ans = 1
        for i in range(k):
            ans*= a[n-i-1]
            ans%= mod
        return ans
    
    for i in range(k//2):
        tmp_min=a[l]*a[l+1]
        tmp_max=a[r]*a[r-1]
        if tmp_max> tmp_min:
            ans*=tmp_max
            ans%=mod
            r-=2
        else:
            ans*= tmp_min
            ans%=mod
            l+=2
    return ans


n, k = map(int, input().split())
A = list(map(int,input().split()))
ans = solve(n,k,A)
print(ans)