Multiplication 4

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

inputFormat

Input

Input is given from Standard Input in the following format:

N K A_1 \ldots A_N

outputFormat

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

样例

4 2
1 2 -3 -4

12