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.util.Scanner;

public class LizardsandBasements2 {

	public static void main(String[] args) {
		Scanner s = new Scanner(System.in);
		int n = s.nextInt();
		int a = s.nextInt();
		int b = s.nextInt();
		StringBuilder out = new StringBuilder();
		
		//3<= n <=10
		int[] h = new int[n+1];;
		for (int i=1;i<=n;i++){
			h[i] = s.nextInt() + 1;
		}
		
		//handle special case of n==3 where there is only one spot you can attack
        if(n == 3){
            int x,y,z, maxNb;
            x = hits(h[1], b); //find hits to kill archer 1
            y = hits(h[2], a); //find hits to kill archer 2
            z = hits(h[3], b); //find hits to kill archer 3
            maxNb = Math.max(Math.max(x,y),z);
            out.append(maxNb);
            out.append("\n");
            for(int i=0; i<maxNb;i++){
                out.append("2 ");
            }
            System.out.println(out.toString());
            s.close();
            return;         
        }
        
        //kill the unreachable outer archers
        int hits1 = hits(h[1],b); //number of hits to kill the left most unreachable archer
        int hits2 = hits(h[n],b); //number of hits to kill the right most unreachable archer
        h[1] = 0;
        h[n] = 0;
        //direct hit damage
        h[2] = Math.max(0, h[2] - hits1 * a);
        h[n-1] = Math.max(0, h[n-1] - hits2 * a);
        //splash damage
        h[3] = Math.max(0, h[3] - hits1 * b);
        h[n-2] = Math.max(0, h[n-2] - hits2 * b);
        
        //this will be used to track possible hit combinations
        int[][][] dp = new int[n+1][17][17];
        int[][] a2 = new int[17][17];//hit on archer2
        int[][] a3 = new int[17][17];//hit on archer3
        
        //precomputer dp[3]
        for(int i=0; i<=h[2]; i++) {
            for(int j=0; j<=h[3]; j++){
                if(i==0 && j==0)
                    continue;
                if(i >= j){
                    int h1 = Math.max(0, i-a);
                    int h2 = Math.max(0, j-b);
                    a2[i][j] = a2[h1][h2]+1;
                    a3[i][j] = a3[h1][h2];
                }
                else{
                    int h1 = Math.max(0, i-b);
                    int h2 = Math.max(0, j-a);
                    a2[i][j] = a2[h1][h2];
                    a3[i][j] = a3[h1][h2]+1;
                }
                dp[3][i][j] = a2[i][j] + a3[i][j];
            }
        }
        
        int[][][] p = new int[n+1][17][17]; //track
        
        for(int ar = 4; ar<n; ar++){ //pointer to current archer
            for(int i = 0; i<=h[ar-1]; i++){ //health of archer[ar-1]
                for(int j=0; j<=h[ar]; j++){  //health of archer[ar]
                    int h1, h2;
                    if(j==0){
                        h1 = h[ar-2];
                        h2 = i;
                        dp[ar][i][j] =  dp[ar-1][h1][h2];                       
                    }
                    else{
                        int hit1 = hits(j, b);
                        h1 = Math.max(0, h[ar-2]-hit1 * b);
                        h2 = Math.max(0, i - hit1 * a);
                        
                        dp[ar][i][j] = dp[ar-1][h1][h2]+hit1;
                        p[ar][i][j] = hit1;
                        
                        h1 = Math.max(0, i-b); 
                        h2 = Math.max(0, j-a);
                        if(dp[ar][i][j] > dp[ar][h1][h2] +1){ //take min of two choices
                            dp[ar][i][j] = dp[ar][h1][h2] +1;
                            p[ar][i][j] = -1; //mark combination
                        }
                    }
                }
            }
        }
        
        int count = dp[n-1][h[n-2]][h[n-1]] + hits1 + hits2; //total hits required for min;
        //create first line output
        out.append(count);
        out.append("\n");
        
        //list hits to kill outlier archers
        for(int i=0; i<hits1; i++){
            out.append("2 ");
        }
        for(int i=0; i<hits2; i++){
            out.append(n-1);
            out.append(" ");
        }
        
        int ar = n-1;
        int i = h[ar-1];
        int j = h[ar];
        
        //add hits for main archers
        while(ar>3){
            int c = p[ar][i][j];
            int h1, h2;
            if(c == 0)
            {
                h1 = h[ar-2];
                h2 = i;
                ar--;
            }
            else if(c>0){
                for(int k = 0; k<c; k++){
                    out.append(ar-1).append(" ");                   
                }
                h1 = Math.max(0,  h[ar-2] - b * c);
                h2 = Math.max(0,  i - a * c);
                ar--;
            }
            else {
                out.append(ar).append(" ");
                h1 = Math.max(0, i-b);
                h2 = Math.max(0, j-a);
            }
            
            i = h1;
            j = h2;
            
        }
        //add earlier computed hits
        for(int k = 0; k< a3[i][j]; k++){
            out.append(3).append(" ");
        }
        for(int k = 0; k< a2[i][j]; k++){
            out.append(2).append(" ");
        }
        
        System.out.println(out.toString());
		s.close();
	}

	private static int hits(int health, int damage) {
		return (int) Math.ceil((double)health/damage);
	}

}
