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
n,k = map(int,input().split())
a = sorted(list(map(int,input().split())))
mod = 10**9 + 7
ans = 1

if n == k:
    for x in a:
        ans *= x
        ans %= mod
    print(ans)
    exit()

b = []
c = []
for x in a:
    if 0 <= x:
        b += [x]
    else:
        c += [x]

if len(b) == 0 and k % 2 == 1:
    c.reverse()
    for i in range(k):
        ans *= c[i]
        ans %= mod
    print(ans)
    exit()

b.reverse()
bi = 0
ci = 0
bl = len(b)
cl = len(c)
if k % 2 == 1:
    ans *= b[0]
    bi += 1
    k -= 1
while k > 0:
    if bl-1 <= bi:
        ans *= c[ci] * c[ci+1]
        ans %= mod
        ci += 2
    elif cl-1 <= ci:
        ans *= b[bi] * b[bi + 1]
        ans %= mod
        bi += 2
    else:
        if b[bi] * b[bi + 1] < c[ci] * c[ci + 1]:
            ans *= c[ci] * c[ci + 1]
            ans %= mod
            ci += 2
        else:
            ans *= b[bi] * b[bi + 1]
            ans %= mod
            bi += 2
    k -= 2
print(ans)