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.*;
import java.io.*;

public class Solution {
	public static PrintWriter w = new PrintWriter(System.out);
	public static int[][][] dp = new int[20][20][20];
	public static int[][][] num = new int[20][20][20];
	public static int[][][] hlth = new int[20][20][20];
	public static int n,a,b;
	public static int[] h;
	public static ArrayList<Integer> res = new ArrayList<>();
	public static int INF = 100000000;
	public static void main(String args[] ) throws Exception {
		Reader in = new Reader();
		n = in.nextInt();
		a = in.nextInt();
		b = in.nextInt();
		h = new int[n];
		for(int[][] i : dp)
			for(int[] j : i)
				Arrays.fill(j,-1);
		for (int i=0; i<n; i++) {
			h[i] = in.nextInt();
			h[i]++;
		}
		while(h[0] > 0) {
			h[0] -= b;
			h[1] -= a;
			h[2] -= b;
			res.add(1);
		}
		h[0] = Math.max(0,h[0]);
		h[1] = Math.max(0,h[1]);
		h[2] = Math.max(0,h[2]);

		while(h[n-1] > 0) {
			h[n-2] -= a;
			h[n-1] -= b;
			h[n-3] -= b;
			res.add(n-2);
		}
		h[n-2] = Math.max(0,h[n-2]);
		h[n-1] = Math.max(0,h[n-1]);
		h[n-3] = Math.max(0,h[n-3]);

		rec(1,h[0],0);

		compute_ans(1,h[0],0);
		w.println(res.size());
		for (int i : res)
			w.print((i+1) + " ");
		w.println();
		w.flush();
		return;
	}
	public static int rec(int i, int j, int k) {
		if(i == n-1) {
			if(j > 0)
				return INF;
			else
				return 0;
		}
		int ans = dp[i][j][k];
		if(ans != -1)
			return ans;
		ans = INF;
		int hh = h[i] - k*b;
		for (int x = 0; x<=16; x++) {
			if(x*b < j)
				continue;
			int nh = Math.max(0,hh - x*a);
			int kk = rec(i+1,nh,x) + x;
			if(kk < ans) {
				ans = kk;
				dp[i][j][k] = ans;
				num[i][j][k] = x;
				hlth[i][j][k] = nh;
			}
		}
		return ans;
	}
	public static void compute_ans(int i, int j, int k) {
		if(i == n -1)
			return;
		int m = num[i][j][k];
		while(m-- > 0)
			res.add(i);
		compute_ans(i+1,hlth[i][j][k],num[i][j][k]);
	}
}

class Reader {
	final private int BUFFER_SIZE = 1 << 16;
	private DataInputStream din;
	private byte[] buffer;
	private int bufferPointer, bytesRead;

	public Reader() {
		din = new DataInputStream(System.in);
		buffer = new byte[BUFFER_SIZE];
		bufferPointer = bytesRead = 0;
	}
	public String nextLine() throws IOException {
		int c = read();
		while(isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while(!isEndOfLine(c));
		return res.toString();
	}
	public String next() throws IOException {
		int c = read();
		while(isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while(!isSpaceChar(c));
		return res.toString();
	}
	public int nextInt() throws IOException {
		int ret = 0;
		byte c = read();
		while(c <= ' ')
			c = read();
		boolean neg = (c == '-');
		if(neg)
			c = read();
		do {
			ret = ret * 10 + c - '0';
		} while((c = read()) >= '0' && c <= '9');
		if (neg)
			return -ret;
		return ret;
	}
	public int[] nextIntArray(int n) throws IOException {
		int a[] = new int[n];
		for(int i = 0; i < n; i++)
			a[i] = nextInt();
		return a;
	}
	public int[][] next2dIntArray(int n, int m) throws IOException {
		int a[][] = new int[n][m];
		for(int i = 0; i < n; i++)
			for(int j = 0; j < m; j++)
				a[i][j] = nextInt();
		return a;
	}
	public char nextChar() throws IOException {
		return next().charAt(0);
	}
	public long nextLong() throws IOException {
		long ret = 0;
		byte c = read();
		while(c <= ' ')
			c = read();
		boolean neg = (c == '-');
		if(neg)
			c = read();
		do {
			ret = ret * 10 + c - '0';
		} while((c = read()) >= '0' && c <= '9');
		if (neg)
			return -ret;
		return ret;
	}
	public double nextDouble() throws IOException {
		double ret = 0, div = 1;
		byte c = read();
		while(c <= ' ')
			c = read();
		boolean neg = (c == '-');
		if(neg)
			c = read();
		do {
			ret = ret * 10 + c - '0';
		} while((c = read()) >= '0' && c <= '9');
		if (c == '.') {
			while((c = read()) >= '0' && c <= '9') {
				ret += (c - '0') / (div *= 10);
			}
		}
		if(neg)
			return -ret;
		return ret;
	}
	private void fillBuffer() throws IOException {
		bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
		if(bytesRead == -1)
			buffer[0] = -1;
	}
	private byte read() throws IOException {
		if(bufferPointer == bytesRead)
			fillBuffer();
		return buffer[bufferPointer++];
	}
	public void close() throws IOException {
		if(din == null)
			return;
		din.close();
	}
	public boolean isSpaceChar(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}
	private boolean isEndOfLine(int c) {
		return c == '\n' || c == '\r' || c == -1;
	}
}