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 = tuple(map(int, input().split()))
MOD = 10 ** 9 + 7

if K == N:
    ans = 1
    for x in A:
        ans = (ans * x) % MOD
    print(ans)
    exit()

plus, minus = [], []
for a in A:
    if a >= 0:
        plus.append(a)
    else:
        minus.append(a)

plus.sort(reverse=True)
minus.sort()

if not plus:
    ans = 1
    if K % 2:
        # 答えは負値になるので絶対値小さいのを取る
        for x in minus[-K:]:
            ans = (ans * x) % MOD
    else:
        # 答えは非負値になるので絶対値大きいのを取る
        for x in minus[:K]:
            ans = (ans * x) % MOD
    print(ans)
    exit()

idx = 0
for i in range(2, N, 2):
    if K - i < 0:
        break
    if not len(plus) >= K - i + 2:
        idx += 2
        continue
    if len(minus) >= i:
        if minus[i - 2] * minus[i - 1] < plus[K - i + 1] * plus[K - i]:
            break
        else:
            idx += 2

ans = 1
for x in minus[:idx] + plus[:K - idx]:
    ans = (ans * x) % MOD
print(ans)
