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.lang.*;
import java.io.*;
import java.text.*;

/* Name of the class has to be "Main" only if the class is public*/
public class CF415C
{
    static class FastReader {
        
        BufferedReader br;
        StringTokenizer st;
        
        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        
        int nextInt() {
            return Integer.parseInt(next());
        }
        
        long nextLong() {
            return Long.parseLong(next());
        }
        
        double nextDouble() {
            return Double.parseDouble(next());
        }
        
        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    
    static class Node {
        
        long pp;
        long a, b;
        
        Node(long x, long y) {
            a = x;
            b = y;
            pp = a * b;
        }
    }
    static class Comp implements Comparator<Node> {
        
        public int compare(Node o1, Node o2) {
            if (o1.pp > o2.pp) {
                return 1;
            } else {
                return -1;
            }
        }
    }
    static int gcd(int x, int y)
    {
        if(y==0) return x;
        else return gcd(y,x%y);
    } 
    static long lcm(int a, int b)
    {
        return (long) (a*b/gcd(a,b));
    }
    static int modInv(int a, int m)
    {
        if(gcd(a,m)!=1) return -999;
        else return (a%m+m)%m;
    }
    static boolean isPowerOfTwo (int x) 
    { 
        return x!=0 && ((x&(x-1)) == 0);          
    } 
    static boolean isprime(int x) 
    {
        for(int i=2;i<=Math.sqrt(x);i++)
        {
            if(x%i==0) return false;
        }
        return true;
    }
    static boolean prime[];
    static final int INT_MAX=1000007;

    static void sieve() {
        prime=new boolean[INT_MAX];
        Arrays.fill(prime,true);
        prime[0]=prime[1]=false;
        for(int i=2;i<=Math.sqrt(INT_MAX);i++)
        {
            if(prime[i]) {
                for(int j=i*2;j<INT_MAX;j+=i)
                prime[j]=false;
            }
        }
    }
    
    public static void main(String[] args) {
        FastReader sc=new FastReader();
        PrintWriter out=new PrintWriter(System.out);
        //your code starts here
        int n=sc.nextInt();
        int k=sc.nextInt();
        int a[]=new int[n];
        int x=k-(n-2)/2;
        if(n==1) {
            if(k==0)
            System.out.println(1);
            else System.out.println(-1);
            return;
        }
        if(x<=0) {
            System.out.println(-1);
            return;
        }
        a[0]=x; a[1]=2*x;
        long sum=x,sum1=0;
        for(int i=2;i<n;i++)
        {
            a[i]=2*x+(i-1); ++sum1;
        }
        sum+=(sum1/2);
        if(sum!=k) out.println(-1);
        else
        {
            for(int i:a) out.print(i+" ");
        }
        out.close();
    }
}