CF1798F.Gifts from Grandfather Ahmed

Grandfather Ahmed's School has $n+1$ students. The students are divided into $k$ classes, and $s_i$ students study in the $i$ -th class. So, $s_1 + s_2 + \ldots + s_k = n+1$ .

Due to the upcoming April Fools' Day, all students will receive gifts!

Grandfather Ahmed planned to order $n+1$ boxes of gifts. Each box can contain one or more gifts. He plans to distribute the boxes between classes so that the following conditions are satisfied:

1. Class number $i$ receives exactly $s_i$ boxes (so that each student can open exactly one box).
2. The total number of gifts in the boxes received by the $i$ -th class should be a multiple of $s_i$ (it should be possible to equally distribute the gifts among the $s_i$ students of this class).

Unfortunately, Grandfather Ahmed ordered only $n$ boxes with gifts, the $i$ -th of which contains $a_i$ gifts.

Ahmed has to buy the missing gift box, and the number of gifts in the box should be an integer between $1$ and $10^6$ . Help Ahmed to determine, how many gifts should the missing box contain, and build a suitable distribution of boxes to classes, or report that this is impossible.

The first line of the input contains two integers $n$ and $k$ ( $1 \le n, k \le 200$ , $k \le n + 1$ ).

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ( $1 \le a_i \le 10^6$ ) — the number of gifts in the available boxes.

The third line contains $k$ integers $s_1, s_2, \ldots, s_k$ ( $1 \le s_i \le n+1$ ) — the number of students in classes. It is guaranteed that $\sum s_i = n+1$ .

If there is no way to buy the remaining box, output the integer $-1$ in a single line.

Otherwise, in the first line, output a single integer $s$ — the number of gifts in the box that Grandfather Ahmed should buy ( $1 \le s \le 10^6$ ).

Next, in $k$ lines, print the distribution of boxes to classes. In the $i$ -th line print $s_i$ integers — the sizes of the boxes that should be sent to the $i$ -th class.

If there are multiple solutions, print any of them.

In the first test, Grandfather Ahmed can buy a box with just $1$ gift. After that, two boxes with $7$ gifts are sent to the first class. $7 + 7 = 14$ is divisible by $2$ . And the second class gets boxes with $1, 7, 127$ gifts. $1 + 7 + 127 = 135$ is evenly divisible by $3$ .

In the second test, the classes have sizes $6$ , $1$ , $9$ , and $3$ . We show that the available boxes are enough to distribute into classes with sizes $6$ , $9$ , $3$ , and in the class with size $1$ , you can buy a box of any size. In class with size $6$ we send boxes with sizes $7$ , $1$ , $7$ , $6$ , $5$ , $4$ . $7 + 1 + 7 + 6 + 5 + 4 = 30$ is divisible by $6$ . In class with size $9$ we send boxes with sizes $1$ , $2$ , $3$ , $8$ , $3$ , $2$ , $9$ , $8$ , $9$ . $1 + 2 + 3 + 8 + 3 + 2 + 9 + 8 + 9 = 45$ is divisible by $9$ . The remaining boxes ( $6$ , $5$ , $4$ ) are sent to the class with size $3$ . $6 + 5 + 4 = 15$ is divisible by $3$ .