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.*;
import java.math.*;

public class Main {

    InputReader ir = new InputReader(System.in);
    PrintWriter out = new PrintWriter(System.out);
    
    void solve() {
        int n = ir.readInt();
        int k = ir.readInt();
        if(k == 0 && n == 1){
            out.println(1);
            return;
        }
        if(k < n/2 || n ==1) {
            out.println(-1);
            return;
        }
        int num = k - (n/2 - 1);
        int last = num;
        int slast = 2*num;
        int arr[] = new int[n];
        int c = 0;
        HashSet <Integer> set = new HashSet();
        set.add(last);
        set.add(slast);
        for(int i = 1; i <= 1000000000 &&  c < n - 2 - (n % 2); i++) {
            if(set.contains(i) == false && set.contains(i + 1) == false) {
                arr[c++] = i;
                arr[c++]= i + 1;
                set.add(i);
                set.add(i + 1);
            }
        }
        arr[c++] = last;
        arr[c++] = slast;
        if(c != n) {
            for(int i = 1; i < 1000000000; i++) {
                if(set.contains(i) == false) {
                    num = i;
                    break;
                }
            }
            arr[c++] = num;
        }
        for(int i = 0; i < n; i++) 
            out.print(arr[i] + " ");
        out.println();
    }

    void run() {
        solve();
        out.close();
    }
    public static void main(String args[]){
        new Main().run();
    }
}

class InputReader {
 
    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;
    private SpaceCharFilter filter;
 
    public InputReader(InputStream stream) {
        this.stream = stream;
    }
 
    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }
    public final int readInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
    }
    public long readLong() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }
 
    public String readString() {
        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 boolean isSpaceChar(int c) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return isWhitespace(c);
    }
        public double readDouble() {
        return Double.parseDouble(readString());
    }
 
    public static boolean isWhitespace(int c) {
        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
 
    public String next() {
        return readString();
    }
 
    public interface SpaceCharFilter {
        public boolean isSpaceChar(int ch);
    }
}