Selecting Numbers 2

Problem Description

Given $N$ numbers, little t wants to select some of them so that the maximum of the selected numbers is less than or equal to $k$ times their average.

Little t wants to select as many numbers as possible. Find how many numbers can never be selected.

Let $M$ be the maximum number of numbers that can be selected. A number can never be selected if and only if it does not appear in any scheme that selects $M$ numbers.

Input Format

The first line contains a positive integer $N$, the number of numbers.

The next line contains $N$ positive integers, the $N$ numbers, separated by spaces.

The last line contains two positive integers $p$ and $q$, representing $k$ ($k = \frac{p}{q}$ and $k > 1$).

Output Format

The first line outputs $M$, the number of numbers that can never be selected.

The next line outputs the $M$ positive integers, the indices of the unselectable numbers in the original sequence, sorted in ascending order, separated by spaces.

Sample Input 1

4
1 2 3 4
3 2

Sample Output 1

0

Sample Input 2

5
1 15 2 5 1
2 1

Sample Output 2

1
2

Sample Input 3

5
1 2 3 1000 10000
4 3

Sample Output 3

2
4 5

Sample Explanation

In sample 1, we can select at most 3 numbers. And for any number, there is a scheme selecting 3 numbers that includes it, so there is no unselectable number.

Constraints

For all data: $1 \le n \le 2 \cdot 10^5$, $0 \le a_i \le 10^9$, $1 \le q < p \le 1000$.

Hint

Some approaches look correct but are actually not quite right. You might want to prove it before coding.