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():
    can_positive = False
    if len(P) > 0:
        if k < n: can_positive = True
        else: can_positive = len(M)%2 == 0
    else: can_positive = k%2 == 0

    if can_positive:
        P.sort()
        M.sort(reverse = True)
        a = [P.pop()] if k%2 else [1]
        while len(P) >= 2: a.append(P.pop() * P.pop())
        while len(M) >= 2: a.append(M.pop() * M.pop())
        return a[:k%2] + sorted(a[1:], reverse = True)[:(k-k%2)//2]
    else: return sorted(P+M, key=lambda x: abs(x))[:k]

n, k = map(int, input().split())
P, M = [], [] # plus, minus
for a in map(int, input().split()):
    if a < 0: M.append(a)
    else: P.append(a)
ans, MOD = 1, 10**9 + 7
for a in solve(): ans *= a; ans %= MOD
ans += MOD; ans %= MOD
print(ans)
