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 = [int(x) for x in input().split()]
A = [int(x) for x in input().split()]

s = [];  t = [];
for a in A:
    if a < 0:
        t.append(a)
    else:
        s.append(a)

P = 10 ** 9 + 7
# 非負にできるか判定
S = len(s)
T = len(t)
ok = False
if S > 0:
    if N == K:
        ok = (T % 2 == 0)
    else:
        ok = True
else:
    ok = (K % 2 == 0)

ans = 1
if not ok:
    A.sort(key = lambda x: abs(x))  # 絶対値小→大
    for i in range(K):
        ans = ans * A[i] % P
else:   # 非負にできる
    s.sort()    # 小→大
    t.sort(reverse = True)  # 絶対値小→大
    if K % 2 == 1:
        ans *= s.pop() # 一番大きい正の数を確保

    p = []
    while len(s) >= 2:
        x = s.pop()
        x = x * s.pop()
        p.append(x)

    while len(t) >= 2:
        x = t.pop()
        x = x * t.pop()
        p.append(x)

    p.sort(reverse = True)
    for i in range(K // 2):
        ans = ans * p[i] % P


print(ans % P)