## Molecules

Petr is working for a company that has built a machine for detecting molecules. Each molecule has a positive integer weight. The machine has a detection range [l, u], where l and u are positive integers. The machine can detect a set of molecules if and only if this set contains a subset of the molecules with total weight belonging to the machine's detection range.

Formally, consider n molecules with weights w0, …, wn − 1. The detection is successful if there is a set of distinct indices I = {i1, … , im} such that lwi1 + … + wimu.

Due to specifics of the machine, the gap between l and u is guaranteed to be greater than or equal to the weight gap between the heaviest and the lightest molecule. Formally, ulwmaxwmin, where wmax = max(w0, …, wn − 1) and wmin = min(w0, …, wn − 1).

Your task is to write a program which either finds any one subset of molecules with total weight within the detection range, or determines that there is no such subset.

You should implement one operation `find_subset`:

• `find_subset(n, l, u, w[])`
• `n`: the number of elements in w (i.e, the number of molecules),
• `l` and `u`: the endpoints of the detection range,
• `w`: weights of the molecules.
• if the required subset exists, then output an array I of indices of molecules that form any one such subset. If there are several correct answers, output any of them.
• if the required subset does not exist, then output a single number 0.

Your program may output the indices in any order.

### Input Format

The input will be given in the following format:

• Line 1: three space-separated integers n, l, u
• Line 2: n space-separated integers w0, …, wn − 1

### Output Format

The output should be in the following format:

• Line 1: a single integer m
• Line 2: m space-separated integers i1, …, im

### Sample Input 1

```4 15 17
6 8 8 7
```

```2
1 2
```

### Explanation 1

In this example we have four molecules with weights 6, 8, 8 and 7. The machine can detect subsets of molecules with total weight between 15 and 17, inclusive. Note, that 17 − 15 ≥ 8 − 6. The total weight of molecules 1 and 3 is w1 + w3 = 8 + 7 = 15, so the program can output [1, 3]. Other possible correct answers are [1, 2] (w1 + w2 = 8 + 8 = 16) and [2, 3] (w2 + w3 = 8 + 7 = 15).

### Sample Input 2

```4 14 15
5 5 6 6
```

```0
```

### Explanation 2

In this example we have four molecules with weights 5, 5, 6 and 6, and we are looking for a subset of them with total weight between 14 and 15, inclusive. Again, note that 15 − 14 ≥ 6 − 5. There is no subset of molecules with total weight between 14 and 15 so the function should return an empty array.

### Sample Input 3

```4 10 20
15 17 16 18
```

```1
0
```

### Explanation 3

In this example we have four molecules with weights 15, 17, 16 and 18, and we are looking for a subset of them with total weight between 10 and 20, inclusive. Again, note that 20 − 10 ≥ 18 − 15. Any subset consisting of exactly one element has total weight between 10 and 20, so the possible correct answers are: , ,  and .

1. (9% of points): 1 ≤ n ≤ 100, 1 ≤ wi ≤ 100, 1 ≤ u, l ≤ 1000, all wi are equal.
2. (10% of points): 1 ≤ n ≤ 100, 1 ≤ wi, u, l ≤ 1000 and max(w0, …, wn − 1) − min(w0, …, wn − 1) ≤ 1.
3. (12% of points): 1 ≤ n ≤ 100 and 1 ≤ wi, u, l ≤ 1000.
4. (15% of points): 1 ≤ n ≤ 10 000 and 1 ≤ wi, u, l ≤ 10 000.
5. (23% of points): 1 ≤ n ≤ 10 000 and 1 ≤ wi, u, l ≤ 500 000.
6. (31% of points): 1 ≤ n ≤ 200 000 and 1 ≤ wi, u, l ≤ 231.

Point Value: 10 (partial)
Time Limit: 2.00s
Memory Limit: 2048M