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.util.*;
import java.io.*;

public class Codeforces {

    

    
    public static void main(String[] args) throws IOException {
        Reader.init(System.in);
        int n = Reader.nextInt(), k = Reader.nextInt();
        
        if(k == 0 && n == 1){
            System.out.println("1");
            return;
        }
        
        if(k < n/2 || n == 1){
            System.out.println("-1");
            return;
        }
        
        int x = k - (n-2)/2;
        StringBuilder ans = new StringBuilder();
        ans.append(x).append(' ').append(x*2).append(' ');
        
        int start  = 0;
        if(x-1 > 1000000000 - x*2)
            start = 1;
        else
            start = x*2+1;
        
        n -= 2;
        for(int i = start; i < start + n; i++)
            ans.append(i).append(' ');
        
        
        System.out.println(ans);
    }
}
class Pair implements Comparable<Pair>{

    int start;
    int end;
    
    @Override
    public int compareTo(Pair t) {
        return this.start - t.start;
    }
    
    Pair(int a, int b){
        start = a;
        end = b;
    }
    
}

class Reader {

    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /**
     * call this method to initialize reader for InputStream
     */
    public static int pars(String x) {
        int num = 0;
        int i = 0;
        if (x.charAt(0) == '-') {
            i = 1;
        }
        for (; i < x.length(); i++) {
            num = num * 10 + (x.charAt(i) - '0');
        }

        if (x.charAt(0) == '-') {
            return -num;
        }

        return num;
    }

    static void init(InputStream input) {
        reader = new BufferedReader(
                new InputStreamReader(input));
        tokenizer = new StringTokenizer("");
    }

    static void init(FileReader input) {
        reader = new BufferedReader(input);
        tokenizer = new StringTokenizer("");
    }

    /**
     * get next word
     */
    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                    reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return pars(next());
    }

    static byte nextByte() throws IOException {

        return Byte.parseByte(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }
}