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.BigInteger;
import java.util.*;


public class JavaApplication7 {
  static  int dr [] = {0,0,1,-1} ;
  static  int dc [] = {1,-1,0,0};
  static int n , m;     
  static char ar [][];
  static  boolean vi [][] ;
static void dfs(int x , int y ,char c)
{
  for(int i = 0 ; i < dr.length; i++)
  { int r = dr[i] + x ; int co = dc[i] + y;
    if(r < n && r >= 0 && co < m && co >=0 && !vi[r][co] && ar[r][co] == '.')
    {vi[r][co] = true ;
     ar[r][co] = c ;
     dfs(r,co,c) ;
    }
  }

}



static int count = 0;
static void dfs(int x , int y )
{
  for(int i = 0 ; i < dr.length; i++)
  { int r = dr[i] + x ; int co = dc[i] + y;
    if(r < n && r >= 0 && co < m && co >=0 && !vi[r][co] && ar[r][co] == '.')
    {vi[r][co] = true ;
     count++;
     dfs(r,co) ;
    }
  }

}
static void dfs2(int x , int y )
{
  for(int i = 0 ; i < dr.length; i++)
  { int r = dr[i] + x ; int co = dc[i] + y;
       
    if(r < n && r >= 0 && co < m && co >= 0 && ar[r][co] == '.')
    {
     vi[r][co] = true ;
     count++;
     ar[r][co] = '*' ;
      
     dfs2(r,co) ;
    }
  }

}
    public static void main(String[] args) throws Exception
    {
      Reader.init(System.in);
      long sum = 0 ;
      
      StringBuilder ans = new StringBuilder() ;
      int n = Reader.nextInt();
      int k = Reader.nextInt() ;
      int w = 5001 ;
      if(n == 1 && k == 0)
        {System.out.println("1");return ;}
     if(n != 1 && k == 0)
         {System.out.println("-1");return ;}
     if(n == 1 && k > 0)
     {System.out.println("-1");return ;}
      if(n % 2 != 0)
      {
      n--;
      int x = k/(n/2) ;
      if(x == 0)
      {System.out.println("-1"); return ;}
      int mod = k%(n/2) ;
      int i = 1;
       for( i = n ; i > 0  ; i-=2)
      {  if(mod > 0)
      { ans.append(((x+1)*i) + " " + ((x+1)*(i-1))+" ") ; mod--;} 
      else 
         ans.append(x*(i) + " " + (x*(i-1))+" ") ; 
      }
          
      ans.append("1000000000") ;
          System.out.println(ans);
         
      }
      else 
      {
      
      int x = k/(n/2) ;
      if(x == 0)
      {System.out.println("-1"); return ;}
      int mod = k%(n/2) ;
      int i = 1;
      for( i = n ; i > 0  ; i-=2)
      {  if(mod > 0)
      { ans.append(((x+1)*i) + " " + ((x+1)*(i-1))+" ") ; mod--;} 
      else 
         ans.append(x*i + " " + (x*(i-1))+" ") ; 
      }
          
     
      
          System.out.println(ans);
      
      
      }
         
    }
       
}
        
    
    
    class pair implements Comparable<pair>
    {
     int  mod,pr , w; 
     String a ;
     
    pair(int a , int b)
    {
    pr = a ;
    mod = b ;
    
    
   
  
    }
    @Override
    public int compareTo(pair t) {
        if(t.pr <pr)
            return 1 ;
        else if(t.pr > pr) return -1 ;
        else return 0 ;
    }
    
    
    
    }

   
    
class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    
    static void init(InputStream input) {
        reader = new BufferedReader(
                     new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }

   
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            
            tokenizer = new StringTokenizer(
                   reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
	
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
    static long nextLong() throws IOException{
    return Long.parseLong(next()) ;
    }
}