Problem: It's holiday. Mashmokh and his boss, Bimokh, are playing a game invented by Mashmokh. 

In this game Mashmokh writes sequence of n distinct integers on the board. Then Bimokh makes several (possibly zero) moves. On the first move he removes the first and the second integer from from the board, on the second move he removes the first and the second integer of the remaining sequence from the board, and so on. Bimokh stops when the board contains less than two numbers. When Bimokh removes numbers x and y from the board, he gets gcd(x, y) points. At the beginning of the game Bimokh has zero points.

Mashmokh wants to win in the game. For this reason he wants his boss to get exactly k points in total. But the guy doesn't know how choose the initial sequence in the right way. 

Please, help him. Find n distinct integers a1, a2, ..., an such that his boss will score exactly k points. Also Mashmokh can't memorize too huge numbers. Therefore each of these integers must be at most 109.

Input

The first line of input contains two space-separated integers n, k (1 ≤ n ≤ 105; 0 ≤ k ≤ 108).

Output

If such sequence doesn't exist output -1 otherwise output n distinct space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109).

Examples

Input

5 2


Output

1 2 3 4 5


Input

5 3

Output

2 4 3 7 1

Input

7 2


Output

-1

Note

gcd(x, y) is greatest common divisor of x and y.

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.io.BufferedWriter;
import java.util.Set;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.util.HashSet;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Mahmoud Aladdin <aladdin3>
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskC solver = new TaskC();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskC {
    public void solve(int testNumber, InputReader jin, OutputWriter jout) {
        int n = jin.int32();
        int k = jin.int32();

        if(k == 0) {
            if(n == 1) {
                jout.println(1);
            } else {
                jout.println(-1);
            }
        } else {
            if(k < (n >> 1)) {
                jout.println(-1);
            } else {
                Set<Integer> arr = new HashSet<Integer>();
                StringBuffer out = new StringBuffer();
                int up = k - (n >> 1);
                for(int b = 1; b <= (n >> 1); b++) {
                    if(up % b > 0) continue;
                    int a = (up / b) + 1;
                    if((2L * a * b) > (int)1e9) continue;
                    if(a <= 0) continue;
                    out.setLength(0); arr.clear();
                    for(int i = 1; i <= (b * 2); i++) {
                        out.append(a * i);
                        out.append(' ');
                        arr.add(a * i);
                    }
                    int c = ((n >> 1) - b);
                    int start = -1;
                    for(int i = 0; i < c; i++) {
                        start += 2;
                        if(arr.contains(start) || arr.contains(start + 1)) {
                            i--;
                            continue;
                        }
                        out.append(start);
                        out.append(' ');
                        out.append(start + 1);
                        out.append(' ');
                        arr.add(start);
                        arr.add(start + 1);
                    }
                    if(n % 2 == 1) {
                        start = 1;
                        while(arr.contains(start)) start++;
                        out.append(start);
                    }
                    jout.println(out);
                    break;
                }
                if(out.length() == 0) {
                    jout.println(-1);
                }
            }
        }
    }
}

class InputReader {
    private static final int bufferMaxLength = 1024;
    private InputStream in;
    private byte[] buffer;
    private int currentBufferSize;
    private int currentBufferTop;
    private static final String tokenizers = " \t\r\f\n";
    
    public InputReader(InputStream stream) {
        this.in = stream;
        buffer = new byte[bufferMaxLength];
        currentBufferSize = 0;
        currentBufferTop = 0;
    }
    
    private boolean refill() {
        try {
            this.currentBufferSize = this.in.read(this.buffer);
            this.currentBufferTop = 0;
        } catch(Exception e) {}
        return this.currentBufferSize > 0;
    }
    
    
    private Byte readChar() {
        if(currentBufferTop < currentBufferSize) {
            return this.buffer[this.currentBufferTop++];
        } else {
            if(!this.refill()) {
                return null;
            } else {
                return readChar();
            }
        }
    }

    public String token()  {
        StringBuffer tok = new StringBuffer();
        Byte first;
        while((first = readChar()) != null && (tokenizers.indexOf((char) first.byteValue()) != -1));
        if(first == null) return null;
        tok.append((char)first.byteValue());
        while((first = readChar()) != null && (tokenizers.indexOf((char) first.byteValue()) == -1)) {
            tok.append((char)first.byteValue());
        }
        return tok.toString();
    }
    
    public Integer int32() throws NumberFormatException {
        String tok = token();
        return tok == null? null : Integer.parseInt(tok);
    }

    }

class OutputWriter {
    private final int bufferMaxOut = 1024;
    private PrintWriter out;
    private StringBuilder output;
    private boolean forceFlush = false;

    public OutputWriter(OutputStream outStream) {
        out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outStream)));
        output = new StringBuilder(2 * bufferMaxOut);
    }

    public OutputWriter(Writer writer) {
        forceFlush = true;
        out = new PrintWriter(writer);
        output = new StringBuilder(2 * bufferMaxOut);
    }

    private void autoFlush() {
        if(forceFlush || output.length() >= bufferMaxOut) {
            flush();
        }
    }

    public void print(Object... tokens) {
        for(int i = 0; i < tokens.length; i++) {
            if(i != 0) output.append(' ');
            output.append(tokens[i]);
        }
        autoFlush();
    }

    public void println(Object... tokens) {
        print(tokens);
        output.append('\n');
        autoFlush();
    }

    public void flush() {
        out.print(output);
        output.setLength(0);
    }

    public void close() {
        flush();
        out.close();
    }
}