Given an array of integers A and a target value val, find all unique combinations of integers from A where their sum is equal to val.

Note: Each integer in the array may be used once in the combination.

Example

A: [10, 1, 2, 7, 6, 1, 5]
val: 8
Combinations: [
  [1, 1, 6],
  [1, 2, 5],
  [1, 7],
  [2, 6]
]

Testing

Input Format

The first line contains an integer ‘T’, denoting the number of test cases.

For each test case the input has three lines:

• An integer ‘n’ denoting the length of the array A.
• n space-separated unique integers denoting the elements of the array A.
• An integer ‘val’ denoting the target value.

Output Format

For each test case, the output has the following lines:

• The first line contains an integer ‘m’ denoting the total no of distinct combinations.
• The next m line contains space-separated integers denoting elements in that particular combination.

Sample Input

3
7
10 1 2 7 6 1 5
8
4
1 2 3 2
4
5
1 2 3 4 5
5

Expected Output

4
1 1 6
1 2 5
1 7
2 6
2
1 3
2 2
3
1 4
2 3
5

Constraints

1 <= T <= 10
1 <= n <= 30
1 <= target <= 500
1 <= Ai <= 500