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.math.*;
import java.util.*;


public class SolutionC {
	public static void main(String[] args){
		try{
			new SolutionC().run();
			//new SolutionC().runIO();
		}
		catch(Exception ex){
			ex.printStackTrace();
		}
	}
	void solve(){
		int n = in.nextInt();
		int k = in.nextInt();
		int y = n/2;
		if( k < y){
			out.println(-1);
			return;
		}
		if( n == 1 && k != 0){
			out.println(-1);
			return;
		}
		int last = 1;
		for(int i = 0; i<y; i++){
			int z = k/(y - i);
			int t1 = (last + z - 1)/z;
			t1 *= z;
			int t2 = t1 + z;

			out.print(t1);
			out.print(' ');
			out.print(t2);
			out.print(' ');
			last = t2 + 1;
			k-=z;
		}
		if(n% 2 == 1) out.println(last);
	}
	PrintWriter out;
	FastScanner in;
	public void run(){
		try{
			in = new FastScanner(System.in);
			out = new PrintWriter(System.out);
			solve();
			out.close();
		}catch(Exception ex){
			ex.printStackTrace();
		}
	}
	public void runIO(){
		try{
			in = new FastScanner(new File("a.in"));
			out = new PrintWriter(new File("a.out"));
			solve();
			out.close();
		}catch(Exception ex){
			ex.printStackTrace();
		}
	}

	class FastScanner{
		BufferedReader bf;
		StringTokenizer st;
		public FastScanner(File is){
			try{
				bf = new BufferedReader(new FileReader(is));
			}catch(Exception ex){
				ex.printStackTrace();
			}
		}
		public FastScanner(InputStream is){
			try{
				bf = new BufferedReader(new InputStreamReader(is));
			}catch(Exception ex){
				ex.printStackTrace();
			}
		}

		String next(){
			while(st == null || !st.hasMoreTokens()){
				try{
					st = new StringTokenizer(bf.readLine());
				}
				catch(Exception ex){
					ex.printStackTrace();
				}
			}
			return st.nextToken();
		}
		int nextInt(){
			return Integer.parseInt(next());
		}
		long nextLong(){
			return Long.parseLong(next());
		}
		double nextDouble(){
			return Double.parseDouble(next());
		}
		float nextFloat(){
			return Float.parseFloat(next());
		}
		BigInteger nextBigInteger(){
			return new BigInteger(next());
		}
		BigDecimal nextBigDecimal(){
			return new BigDecimal(next());
		}	
		int[] nextArray(int n){
			int x[] = new int[n];
			for(int i = 0; i < n; i++){
				x[i] = Integer.parseInt(next());
			}
			return x;
		}
	}
}