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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashSet;
import java.util.Iterator;
import java.util.LinkedHashSet;
import java.util.List;
import java.util.ListIterator;
import java.util.PriorityQueue;
import java.util.Set;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class CopyOfCopyOfSolution {
    private static Integer val = 40;

    /**
     * #235 Div2 Problem D
     * #href: http://codeforces.com/contest/401/problem/D
     *
     * @param args
     * @throws NumberFormatException
     * @throws IOException
     */
    public static void main(final String[] args) throws NumberFormatException, IOException {
        final InputStream inputStream = System.in;
        final OutputStream outputStream = System.out;
        final InputReader in = new InputReader(inputStream);
        final PrintWriter out = new PrintWriter(outputStream);
        final int n = in.nextInt();
        int k = in.nextInt();
        if (k < (n / 2)) {
            out.println(-1);
        } else {
            if (k == 0) {
                out.println("1");
            } else if (n == 1) {
                out.println("-1");
            } else {
                k -= ((n / 2) - 1);
                out.print(k + " ");
                out.print((2 * k) + " ");
                int w = 1;
                int i = 2;
                for (; i < n;) {
                    while ((w == k) || (w == (2 * k)) || ((w + 1) == k) || ((w + 1) == (2 * k))) {
                        w++;
                    }
                    out.print(w++ + " ");
                    i++;
                    if (i < n) {
                        out.print(w++ + " ");
                    }
                    i++;
                }
                if (i < n) {
                    out.print(w++ + " ");
                }
                out.println();
            }
        }
        out.close();
    }

    private static Tree construct(final long[] a, final int from, final int to) {
        final Tree tree = new Tree();
        tree.from = 0;
        tree.to = a.length;
        if ((to - from) == 1) {
            tree.sum = a[from];
        } else {
            tree.left = construct(a, from, (from + to) / 2);
            tree.right = construct(a, (from + to) / 2, to);
            tree.sum = tree.left.sum + tree.right.sum;
        }
        return tree;
    }

    private static class Tree {
        int from;
        int to;
        long sum;
        Tree left;
        Tree right;

        public void update(final int index, final long diff) {
            if (diff == 0) {
                return;
            }
            if ((index >= this.from) && (index < this.to)) {
                this.sum += diff;
                if ((this.right != null)) {
                    this.right.update(index, diff);
                }
                if ((this.left != null)) {
                    this.left.update(index, diff);
                }
            }
        }
    }

    private static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(final InputStream stream) {
            this.reader = new BufferedReader(new InputStreamReader(stream));
            this.tokenizer = null;
        }

        public String next() {
            while ((this.tokenizer == null) || !this.tokenizer.hasMoreTokens()) {
                try {
                    this.tokenizer = new StringTokenizer(this.reader.readLine());
                } catch (final IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return this.tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(this.next());
        }

        public long nextLong() {
            return Long.parseLong(this.next());
        }

        public double nextDouble() {
            return Double.parseDouble(this.next());
        }

    }
}