Count Ways to Fill Time Slots

You are given a collection of songs and several time slots. Each song has a duration and each time slot requires a combination of songs whose total duration exactly matches the slot's duration. Each song can be used at most once in forming a combination and different orders of the same subset of songs are considered identical.

Your task is to determine, for each time slot, the number of distinct ways to pick a subset of songs that perfectly fills the slot.

Note: Because the number of songs is relatively small, you may generate all possible subsets of songs.

Mathematically, for a given slot with required duration \( S \), you need to count how many subsets \( I \subseteq \{1, 2, \dots, N\} \) satisfy \[ \sum_{i \in I} d_i = S \] where \( d_i \) is the duration of the \( i\)-th song.

inputFormat

The input is given from standard input (stdin) and follows this format:

1. The first line contains an integer \( T \) representing the number of test cases.
2. For each test case:
   • The first line contains two integers \( N \) and \( M \), where \( N \) is the number of songs and \( M \) is the number of time slots.
   • The second line contains \( N \) integers, each indicating the duration of a song.
   • The third line contains \( M \) integers, each indicating the required duration of a time slot.

outputFormat

For each test case, output one line containing \( M \) integers separated by a space. Each integer represents the number of ways to achieve the corresponding time slot's required duration using a subset of songs.

## sample

1
4 2
30 40 20 10
50 60

2 2

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