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 A {
    public static long time = 0;
    public static void main(String[] args) throws Exception {
        time = System.currentTimeMillis();
        
        IN = System.in;
        OUT = System.out;
        in = new BufferedReader(new InputStreamReader(IN));
        out = new PrintWriter(OUT, FLUSH);
        solveOne();
        out.flush();
    }
    
    public static void solveOne() throws Exception {
        int n1 = ni();
        int k1 = ni();
        int min = n1 / 2;
        if (n1 == 1){
            if (k1 == 0){
                pn(1);
                return;
            }
            else {
                pn(-1);
                return;
            }
        }
        if (k1 < min){
            pn(-1);
            return;
        }
        
        int extra = k1 - min;
        int mult = (int)1e9 / n1;
        for (int i = n1; i > 1; i -= 2){
            int take = Math.min(extra, mult - 1);
            int times = take + 1;
            extra -= take;
            out.print((i * times) + " " + ((i - 1) * times) + " ");
        }
        if (n1 % 2 == 1){
            out.print(1);
        }
        out.println();
    }
    
    public static void solveTwo() throws Exception {
        
    }
    
    public static void solveThree() throws Exception {
        
    }
    
    public static BufferedReader in;
    public static StringTokenizer st;
    public static InputStream IN;
    public static OutputStream OUT;
    public static String nx() throws Exception {
        for (;st == null || !st.hasMoreTokens();){
            String k1 = in.readLine();
            if (k1 == null) return null;
            st = new StringTokenizer(k1);
        }
        return st.nextToken();
    }
    public static int ni () throws Exception {
        return Integer.parseInt(nx());
    }
    public static long nl() throws Exception{
        return Long.parseLong(nx());
    }
    public static double nd() throws Exception{
        return Double.parseDouble(nx());
    }
    public static void px(Object ... l1){
        System.out.println(Arrays.deepToString(l1));
    }
    public static boolean FLUSH = false;
    public static PrintWriter out;
    public static void p(Object ... l1){
        for (int i = 0; i < l1.length; i++){
            if (i != 0) out.print(' ');
            out.print(l1[i].toString());
        }
    }
    public static void pn(Object ... l1){
        for (int i = 0; i < l1.length; i++){
            if (i != 0) out.print(' ');
            out.print(l1[i].toString());
        }
        out.println();
    }
    
    public static void pn(Collection l1){
        boolean first = true;
        for (Object e: l1){
            if (first) first = false;
            else out.print(' ');
            out.print(e.toString());
        }
        out.println();
    }

}