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.*;
import java.util.*;

import static java.lang.Math.*;

/**
 * @author master_j
 */
public class Solution {
    private IO io;
    private static final String _localArg = "master_j";
    private final String _problemName = "";
    private final int _inMode = IO.STD_;
    private final int _outMode = IO.STD_;
    private final boolean _autoFlush = false;

    private void solve() throws IOException {
        int n = io.nI(), k = io.nI();
        if(n/2 > k || n == 1 && k > 0){
            io.wln(-1);
            return;
        }
        final int N = n;
        boolean oneMore = (n % 2 == 1);
        n /= 2;
        List<Integer> ans = new ArrayList<>(N);
        Set<Integer> used = new HashSet<>();
        if (k > n) {
            int need = k - n + 1;
            ans.add(need);
            ans.add(need * 2);
            used.add(need);
            used.add(need * 2);
            n--;
            k -= need;
        }
        int last = 1;
        while (n > 0) {
            k--;
            n--;
            for (; ; last++)
                if (!used.contains(last) && !used.contains(last + 1)) {
                    used.add(last);
                    used.add(last + 1);
                    ans.add(last);
                    ans.add(last + 1);
                    last++;
                    break;
                }
        }
        if (oneMore)
            for (; ; last++)
                if (!used.contains(last)) {
                    ans.add(last);
                    break;
                }
        for (int i : ans) {
            io.w(i);
            io.w(' ');
        }
        io.wln();
    }//2.2250738585072012e-308

    private void init(boolean local) throws IOException {
        if(local)
            io = new IO(IO._PUT_TXT, IO.STD_);
        else{
            if((_inMode == IO.PROBNAME_ || _outMode == IO.PROBNAME_) && _problemName.length() == 0)
                throw new IllegalStateException("You imbecile. Where's my <_problemName>?");
            io = new IO(_inMode, _outMode);
        }

        long nanoTime = 0;
        if(local){
            nanoTime -= System.nanoTime();
            if(_autoFlush)
                io.wln("NOTE: auto-flush is on.");
            io.wln("<output>");
            io.flush();
        }

        solve();
        io.flush();

        if(local){
            io.wln("</output>");
            nanoTime += System.nanoTime();
            long d9 = 1000000000, d6 = 1000000, d3 = 1000;
            if(nanoTime >= d9)
                io.wf("%d.%d seconds\n", nanoTime/d9, nanoTime%d9);
            else if(nanoTime >= d6)
                io.wf("%d.%d millis\n", nanoTime/d6, nanoTime%d6);
            else if(nanoTime >= d3)
                io.wf("%d.%d micros\n", nanoTime/d3, nanoTime%d3);
            else
                io.wf("%d nanos\n", nanoTime);
            io.flush();
        }

        io.close();
    }

    /**
     * Input-output class
     *
     * @author master_j
     * @version 0.3.2
     */
    private class IO {
//     _____________________________ _________________
//    |  mode  |      from/to       |  variable name  |
//    |--------|--------------------|-----------------|
//    |    0   |      System.*      |       STD_      |
//    |    1   |      *put.txt      |     _PUT_TXT    |
//    |    2   |  <_problemName>.*  |     PROBNAME_   |
//    |________|____________________|_________________|
//

        static final int STD_ = 0;
        static final int _PUT_TXT = 1;
        static final int PROBNAME_ = 2;

        StreamTokenizer st;
        BufferedReader br;
        Reader reader;

        PrintWriter pw;
        Writer writer;

        IO(int inMode, int outMode) throws IOException {
            Locale.setDefault(Locale.US);

            if(inMode == IO.STD_)
                reader = new InputStreamReader(System.in);
            else if(inMode == IO._PUT_TXT)
                reader = new FileReader("input.txt");
            else if(inMode == IO.PROBNAME_)
                reader = new FileReader(_problemName + ".in");
            else
                throw new IllegalStateException("You imbecile. How did you do that?");

            if(outMode == IO.STD_)
                writer = new OutputStreamWriter(System.out);
            else if(outMode == IO._PUT_TXT)
                writer = new FileWriter("output.txt");
            else if(outMode == IO.PROBNAME_)
                writer = new FileWriter(_problemName + ".out");
            else
                throw new IllegalStateException("You imbecille. Why did you do that?");

            br = new BufferedReader(reader);
            st = new StreamTokenizer(br);

            pw = new PrintWriter(writer, _autoFlush);
        }

        void wln()          {pw.println(); }
        void wln(boolean x) {pw.println(x);}
        void wln(char x)    {pw.println(x);}
        void wln(char x[])  {pw.println(x);}
        void wln(double x)  {pw.println(x);}
        void wln(float x)   {pw.println(x);}
        void wln(int x)     {pw.println(x);}
        void wln(long x)    {pw.println(x);}
        void wln(Object x)  {pw.println(x);}
        void wln(String x)  {pw.println(x);}

        void wf(String f, Object...o){pw.printf(f, o);}

        void w(boolean x)   {pw.print(x);}
        void w(char x)      {pw.print(x);}
        void w(char x[])    {pw.print(x);}
        void w(double x)    {pw.print(x);}
        void w(float x)     {pw.print(x);}
        void w(int x)       {pw.print(x);}
        void w(long x)      {pw.print(x);}
        void w(Object x)    {pw.print(x);}
        void w(String x)    {pw.print(x);}

        int nI() throws IOException    {st.nextToken(); return (int)st.nval;}
        double nD() throws IOException {st.nextToken(); return st.nval;}
        float nF() throws IOException  {st.nextToken(); return (float)st.nval;}
        long nL() throws IOException   {st.nextToken(); return (long)st.nval;}
        String nS() throws IOException {st.nextToken(); return st.sval;}

        void wc(String x){ wc(x.toCharArray()); }
        void wc(char c1, char c2){for(char c = c1; c<=c2; c++)wc(c);}
        void wc(char x[]){
            for(char c : x)
                wc(c);
        }
        void wc(char x){st.ordinaryChar(x); st.wordChars(x, x);}

        public boolean eof() {return st.ttype == StreamTokenizer.TT_EOF;}
        public boolean eol() {return st.ttype == StreamTokenizer.TT_EOL;}

        void flush(){pw.flush();}
        void close() throws IOException{reader.close(); br.close(); flush(); pw.close();}
    }

    public static void main(final String args[]) throws IOException {
        new Solution().init(args.length == 1 && args[0].equals(_localArg));
    }
}