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$ curl repovive.com/contests/10000/problems/D1B

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Full Enough (Hard Version) - Weekly Challenge 1: Approximation | Repovive | Repovive

W1D1B. Full Enough (Hard Version)

2 pts1s256 MB

You are given $n$ stones. The weight of stone $i$ is $w_i$ .

You have a bag with capacity $W$ . You may choose any subset of stones whose total weight is at most $W$ .

It is guaranteed that there exists a non-empty subset of stones whose total weight is exactly $W$ .

You do not need to find such an exact subset. You only need to choose a subset whose total weight is at least $90\%$ of $W$ and at most $W$ .

Constraints

$1 \le t \le 5$
$1 \le n \le 750$
The sum of $n$ over all test cases is at most $750$
$1 \le W \le 10^{12}$
$1 \le w_i \le W$
There exists a non-empty subset with total weight exactly $W$

Input

The input is given in the following format:

t

\left. \begin{array}{l} n \quad W \\ w_1 \quad w_2 \quad \cdots \quad w_n \end{array} \right\} \times t

Output

For each test case, first output an integer $k$ , the number of chosen stones.

Then output $k$ distinct integers $i_1,i_2,\ldots,i_k$ , the indices of the chosen stones.

The total weight of the chosen stones must be at most $W$ and at least $90\%$ of $W$ .

The output format is:

\left. \begin{array}{l} k \\ i_1 \quad i_2 \quad \cdots \quad i_k \end{array} \right\} \times t

If $k=0$ , the second line may be empty.

Samples

Input

1
8 100
45 45 60 40 30 20 15 5

Explanation

The chosen stones have total weight $45+45=90$ .

This does not fill the bag exactly, but it is still valid because $90$ is exactly $90\%$ of $100$ and does not exceed the capacity.

Output

2
1 2

You are given $n$ stones. The weight of stone $i$ is $w_i$ .

You have a bag with capacity $W$ . You may choose any subset of stones whose total weight is at most $W$ .

It is guaranteed that there exists a non-empty subset of stones whose total weight is exactly $W$ .

You do not need to find such an exact subset. You only need to choose a subset whose total weight is at least $90\%$ of $W$ and at most $W$ .

$1 \le t \le 5$
$1 \le n \le 750$
The sum of $n$ over all test cases is at most $750$
$1 \le W \le 10^{12}$
$1 \le w_i \le W$
There exists a non-empty subset with total weight exactly $W$

The input is given in the following format:

t

\left. \begin{array}{l} n \quad W \\ w_1 \quad w_2 \quad \cdots \quad w_n \end{array} \right\} \times t

For each test case, first output an integer $k$ , the number of chosen stones.

Then output $k$ distinct integers $i_1,i_2,\ldots,i_k$ , the indices of the chosen stones.

The total weight of the chosen stones must be at most $W$ and at least $90\%$ of $W$ .

The output format is:

\left. \begin{array}{l} k \\ i_1 \quad i_2 \quad \cdots \quad i_k \end{array} \right\} \times t

If $k=0$ , the second line may be empty.

The chosen stones have total weight $45+45=90$ .

This does not fill the bag exactly, but it is still valid because $90$ is exactly $90\%$ of $100$ and does not exceed the capacity.

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W1D1B. Full Enough (Hard Version)

Constraints

Input

Output

Samples

W1D1B. Full Enough (Hard Version)

Constraints

Input

Output

Samples