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.awt.geom.QuadCurve2D;
import java.io.*;
import java.util.*;
import java.lang.StringBuilder;

public class Main {
    static PrintWriter out = new PrintWriter(System.out);
    static String INPUT = "";
    static InputStream inStream = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());

    static int n;
    static int a;
    static int b;
    static int[] healths;
    static ArrayDeque Q = new ArrayDeque<Integer>(); //keep track of the archers we hit
    static ArrayDeque Q2 = new ArrayDeque<Integer>();
    public static void killFandL(){
        while(healths[1]>=0){
            healths[1]-=b;
            healths[2]-=a;
            healths[3]-=b;
            Q.push(2);//we hit 2
        }
        while(healths[n]>=0){
            healths[n-2]-=b;
            healths[n-1]-=a;
            healths[n]-=b;
            Q.push(n-1);
        }
    }

    public static void makeInitialSol(){
        for (int i=2; i<n; i++){
            for(int j=0; j<=healths[i]/a; j++){
                //attack each archer until it is dead no matter what
                Q.push(i);
            }
        }
    }

    public static void bf(int curA){

        //if we are at the last archer and all others are dead
        if(curA==n){
            if(Q.size() > Q2.size()){
                Q = new ArrayDeque<Integer>(Q2);
            }
            return;
        }

        int fb=0;
        //hit curA with fire until archer to left is dead
        while(healths[curA-1] >= 0){
            healths[curA-1]-=b;
            healths[curA]-=a;
            healths[curA + 1] -= b;

            fb++;
            Q2.push(curA);
        }
        //now kill curA
        //we can do this by hitting cubf
        //or curA+1
        while(healths[curA]>=0){
            //try it both ways and Q will keep track of shortest in the end
            bf(curA+1);
            healths[curA-1]-=b;
            healths[curA]-=a;
            healths[curA+1]-=b;
            fb++;
            Q2.push(curA);
        }

        //now that curA is dead, move on
        bf(curA+1);
        //undo on way back
        healths[curA-1]+=fb*b;
        healths[curA]+=fb*a;
        healths[curA+1]+=fb*b;
        while(fb-- > 0){
            Q2.pop();
        }
    }

    public static void printSol(){
        out.println(Q.size());
        while(!Q.isEmpty()){
            out.print(Q.pop());
            out.print(' ');
        }
    }

    public static void main(String[] args) throws IOException {
        n = nextInt();
        a = nextInt();
        b = nextInt();
        healths = nextArray1(n);

        killFandL();
        Q2 = new ArrayDeque(Q); //save starting state
        //find any solution
        makeInitialSol();
        //start at 2 and move through line
        bf(2);
        printSol();
        out.flush();

    }


    private static boolean eof() {
        if (lenbuf == -1) return true;
        int lptr = ptrbuf;
        while (lptr < lenbuf) if (!isSpaceChar(inbuf[lptr++])) return false;
        try {
            inStream.mark(1000);
            while (true) {
                int b = inStream.read();
                if (b == -1) {
                    inStream.reset();
                    return true;
                } else if (!isSpaceChar(b)) {
                    inStream.reset();
                    return false;
                }
            }
        } catch (IOException e) {
            return true;
        }
    }

    private static byte[] inbuf = new byte[1024];
    static int lenbuf = 0, ptrbuf = 0;

    private static int readByte() {
        if (lenbuf == -1) throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = inStream.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0)
                return -1;
        }
        return inbuf[ptrbuf++];
    }

    private static boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }

    private static int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
        return b;
    }

    private static double nextDouble() {
        return Double.parseDouble(nextString());
    }

    private static char nextChar() {
        return (char) skip();
    }

    private static String nextString() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private static char[] nextString(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private static char[][] nextMap(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++)
            map[i] = nextString(m);
        return map;
    }

    private static int[] nextArray0(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = nextInt();
        return a;
    }

    private static int[] nextArray1(int n) {
        int[] a = new int[n + 1];
        for (int i = 1; i <= n; i++)
            a[i] = nextInt();
        return a;
    }

    private static long[] nextArrayLong1(int n) {
        long[] a = new long[n + 1];
        for (int i = 1; i <= n; i++)
            a[i] = nextLong();
        return a;
    }

    private static long[] nextArrayLong0(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = nextLong();
        return a;
    }

    private static int nextInt() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private static long nextLong() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
}
