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
# E - Multiplication 4
import heapq
N, K = map(int, input().split())
A = list(int(a) for a in input().split())
MOD = 10**9 + 7


if N == K:
    ans = 1
    for a in A:
        ans = (ans * a) % MOD
else:
    pos = []
    neg = []
    for a in A:
        if a >= 0:
            pos.append(a)
        else:
            neg.append(a)

    if len(neg) == N and K&1 == 1:
        neg.sort(reverse=True)
        ans = 1
        for i in range(K):
            ans = (ans * neg[i]) % MOD
    else:
        pos.sort(reverse=True)
        dbl = []
        ans = 1
        ini = 0
        rem = K
        if K&1 == 1:
            ans = (ans * pos[0]) % MOD
            ini = 1
            rem -= 1
        for i in range(0, (len(pos)-ini)//2):
            heapq.heappush(dbl, (pos[ini+i*2] * pos[ini+i*2+1])*-1)
        neg.sort()
        for i in range(0, len(neg)//2):
            heapq.heappush(dbl, (neg[i*2] * neg[i*2+1]) * -1)
        while rem > 0:
            ans = (ans * heapq.heappop(dbl) * -1) % MOD
            rem -= 2

print(ans)