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

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