 Competitions

# Detecting Molecules

Time limit 1 second
Memory limit 128 MiB

Peter 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 w_0, ..., w_{n-1}. The detection is successful if there is a set of distinct indices I = i_1, ..., i_m such that l ≤ w_{i_1} + .. + w_{i_m} \le u.

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 u - l \ge w_{max} - w_{min}, where w_{max} = max(w_0, ..., w_{n-1}) and w_{min} = min(w_0, ..., w_{n-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.

## Input data

First line contains three integers: the number of molecules n~(1 \le n \le 200000) and the endpoints of the detection range l and u~(1 \le l, u < 2^{31}). Second line contains n integers: w_0, ..., w_{n-1}~(1 \le w_i < 2^{31}).

## Output data

Print in the first line the size of subset m. Print in the second line the indices of molecules that form any one such subset. If there are several correct answers, print any of them.

## Examples

Input example #1
4 15 17
6 8 8 7

Output example #1
2
2 1

Input example #2
4 14 15
5 5 6 6

Output example #2
0


Input example #3
4 10 20
15 17 16 18

Output example #3
1
3

Source 2016 IOI Kazan, Russia, Day 1