This is simplified version of the problem used on the original contest. The original problem seems to have too difiicult solution. The constraints for input data have been reduced.

Polycarp likes to play computer role-playing game «Lizards and Basements». At the moment he is playing it as a magician. At one of the last levels he has to fight the line of archers. The only spell with which he can damage them is a fire ball. If Polycarp hits the i-th archer with his fire ball (they are numbered from left to right), the archer loses a health points. At the same time the spell damages the archers adjacent to the i-th (if any) — they lose b (1 ≤ b < a ≤ 10) health points each.

As the extreme archers (i.e. archers numbered 1 and n) are very far, the fire ball cannot reach them. Polycarp can hit any other archer with his fire ball.

The amount of health points for each archer is known. An archer will be killed when this amount is less than 0. What is the minimum amount of spells Polycarp can use to kill all the enemies?

Polycarp can throw his fire ball into an archer if the latter is already killed.

Input

The first line of the input contains three integers n, a, b (3 ≤ n ≤ 10; 1 ≤ b < a ≤ 10). The second line contains a sequence of n integers — h1, h2, ..., hn (1 ≤ hi ≤ 15), where hi is the amount of health points the i-th archer has.

Output

In the first line print t — the required minimum amount of fire balls.

In the second line print t numbers — indexes of the archers that Polycarp should hit to kill all the archers in t shots. All these numbers should be between 2 and n - 1. Separate numbers with spaces. If there are several solutions, output any of them. Print numbers in any order.

Examples

Input

3 2 1
2 2 2


Output

3
2 2 2 

Input

4 3 1
1 4 1 1


Output

4
2 2 3 3 
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.Deque;

public class Main {
	
	static int[] archers;
	static Deque<Integer> shots;
	static Deque<Integer> test;
	static int n;
	static int a;
	static int b;

	public static void main(String[] args) throws IOException {
		/* Read in from console */
		BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
		PrintWriter writer = new PrintWriter(System.out);
		
		String[] data = reader.readLine().split("\\s");
		n = Integer.parseInt(data[0]);
		a = Integer.parseInt(data[1]);
		b = Integer.parseInt(data[2]);
		
		archers = new int[n+1];
		shots = new ArrayDeque<Integer>();
		
		data = reader.readLine().split("\\s");
		for(int i = 1; i<=n; i++){
			archers[i] = Integer.parseInt(data[i-1]);
		}
		
		//only way to kill ends
		while(archers[1] >= 0){
			archers[2] -= a;
			archers[1] -= b;
			archers[3] -= b;
			shots.push(2);
		}
		
		while(archers[n] >= 0){
			archers[n-1] -= a;
			archers[n] -= b;
			archers[n-2]-= b;
			shots.push(n-1);
		}
		
		test = new ArrayDeque<Integer>(shots);
		
		//worst case shoot every other one no matter what
		for(int i=2; i<n-1; i++){
			int temp = archers[i];
			while(temp >= 0){
				shots.push(i);
				temp -= a;
			}
		}
		
		//kill rest
		killEm(2);
		
		writer.println(shots.size());	
		for(Integer i:shots)
			writer.print(i + " ");
		
		writer.close();
	}
	
	public static void killEm(int index){
		//base case
		if(index == n && archers[index-1] < 0){
			//save best option so far
			if(shots.size() > test.size())
				shots = new ArrayDeque<Integer>(test);
			return;
		}
		
		int numberShots = 0;
		
		while(archers[index-1] >= 0){
			archers[index] -= a;
			archers[index-1] -= b;
			archers[index+1] -=b;
			test.push(index);
			numberShots++;
		}
		while(archers[index] >= 0){
			//recursive call to see if the previous loop is minimum or not
			killEm(index+1);
			
			archers[index] -= a;
			archers[index-1] -=b;
			archers[index+1] -=b;
			test.push(index);
			numberShots++;
		}
		
		//recursive call for next archer
		killEm(index+1);
		
		//reset before next try
		for(int i=0; i<numberShots; i++){
			test.pop();
			archers[index] += a;
			archers[index+1] += b;
			archers[index-1] += b;
		}
	}
}
