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 code5 {
	InputStream is;
	PrintWriter out;
	static long mod=pow(10,9)+7;
	static final int max=100000;
	static int dx[]={1,-1,-1,1,0,0,1,-1},dy[]={1,-1,1,-1,1,-1,0,0};
	ArrayList<Integer> p;
	void solve()
	{
		p=new ArrayList<Integer>();
		prime();
		int n=ni();
		int k=ni();
		if(n==1)
		{
			if(k==0)
				out.println("1");
			else
				out.println("-1");
			return;
		}
		int after=n/2-1;
		if(after>=k)
		{
			out.println("-1");
			return;
		}
		out.print(k-after+" "+2*(k-after));
		for(int i=0,c=0;c<n-2;i++)
		{
			if(p.get(i)!=(k-after)&&p.get(i)!=2*(k-after))
			{
				out.print(" "+p.get(i++));
				c++;
			}
			
		}
	}
	public void prime()
	{
		int n=10000000;
		boolean prime[]=new boolean[n+1];
		prime[0]=true;
		for(int i=2;i*i<=n;i++)
		{
			if(prime[i])
				continue;
			for(int j=i;j*i<=n;j++)
			{
				prime[i*j]=true;
			}
		}
		for(int i=3;i<=n;i++)
		{
			if(!prime[i])
				p.add(i);
		}
	}
	public static int count(int x)
	{
		int num=0;
		while(x!=0)
		{
			x=x&(x-1);
			num++;
		}
		return num;
	}
	static long d, x, y;
	void extendedEuclid(long A, long B) {
	    if(B == 0) {
	        d = A;
	        x = 1;
	        y = 0;
	    }
	    else {
	        extendedEuclid(B, A%B);
	        long temp = x;
	        x = y;
	        y = temp - (A/B)*y;
	    }
	}
	long modInverse(long A,long M) //A and M are coprime
	{
	    extendedEuclid(A,M);
	    return (x%M+M)%M;    //x may be negative
	}
	public static void mergeSort(int[] arr, int l ,int r){
		if((r-l)>=1){
			int mid = (l+r)/2;
			mergeSort(arr,l,mid);
			mergeSort(arr,mid+1,r);
			merge(arr,l,r,mid);
		}
	}
	public static void merge(int arr[], int l, int r, int mid){
		int n1 = (mid-l+1), n2 = (r-mid);
		int left[] = new int[n1];
		int right[] = new int[n2];
		for(int i =0 ;i<n1;i++) left[i] = arr[l+i];
		for(int i =0 ;i<n2;i++) right[i] = arr[mid+1+i];
		int i =0, j =0, k = l;
		while(i<n1 && j<n2){
			if(left[i]>right[j]){
				arr[k++] = right[j++];
			}
			else{
				arr[k++] = left[i++];
			}
		}
		while(i<n1) arr[k++] = left[i++];
		while(j<n2) arr[k++] = right[j++];
	}
	public static void mergeSort(long[] arr, int l ,int r){
		if((r-l)>=1){
			int mid = (l+r)/2;
			mergeSort(arr,l,mid);
			mergeSort(arr,mid+1,r);
			merge(arr,l,r,mid);
		}
	}
	public static void merge(long arr[], int l, int r, int mid){
		int n1 = (mid-l+1), n2 = (r-mid);
		long left[] = new long[n1];
		long right[] = new long[n2];
		for(int i =0 ;i<n1;i++) left[i] = arr[l+i];
		for(int i =0 ;i<n2;i++) right[i] = arr[mid+1+i];
		int i =0, j =0, k = l;
		while(i<n1 && j<n2){
			if(left[i]>right[j]){
				arr[k++] = right[j++];
			}
			else{
				arr[k++] = left[i++];
			}
		}
		while(i<n1) arr[k++] = left[i++];
		while(j<n2) arr[k++] = right[j++];
	}
	 static class Pair implements Comparable<Pair>{
		 
	       int x,y,k,i;
	        
		Pair (int x,int y){
			this.x=x;
			this.y=y;
		}
	        
		public int compareTo(Pair o) {
					return this.x-o.x;
		}
	 
	        public boolean equals(Object o) {
	            if (o instanceof Pair) {
	                Pair p = (Pair)o;
	                return p.x == x && p.y == y && p.k==k;
	            }
	            return false;
	        }
	           
	 
	        @Override
	        public String toString() {
	            return  "("+x + " " + y +" "+k+" "+i+" )";
	        }
	    
	    } 
	    
	    public static boolean isPal(String s){
	        for(int i=0, j=s.length()-1;i<=j;i++,j--){
	                if(s.charAt(i)!=s.charAt(j)) return false;
	        }
	        return true;
	    }
	    public static String rev(String s){
			StringBuilder sb=new StringBuilder(s);
			sb.reverse();
			return sb.toString();
	    }
	    
	    public static long gcd(long x,long y){
		if(x%y==0)
			return y;
		else
			return gcd(y,x%y);
	    }
	    
	    public static int gcd(int x,int y){
	    	if(y==0) 
	    		return x; 
	    	return gcd(y,x%y);
	    }
	    
	    public static long gcdExtended(long a,long b,long[] x){
	        
	        if(a==0){
	            x[0]=0;
	            x[1]=1;
	            return b;
	        }
	        long[] y=new long[2];
	        long gcd=gcdExtended(b%a, a, y);
	        
	        x[0]=y[1]-(b/a)*y[0];
	        x[1]=y[0];
	        
	        return gcd;
	    }
	    
	    public static int abs(int a,int b){
		return (int)Math.abs(a-b);
	    }
	 
	    public static long abs(long a,long b){
		return (long)Math.abs(a-b);
	    }
	    
	    public static int max(int a,int b){
		if(a>b)
			return a;
		else
			return b;
	    }
	 
	    public static int min(int a,int b){
		if(a>b)
			return b;
		else 
			return a;
	    }
	    
	    public static long max(long a,long b){
		if(a>b)
			return a;
		else
			return b;
	    }
	 
	    public static long min(long a,long b){
		if(a>b)
			return b;
		else 
			return a;
	    }
	 
	    public static long pow(long n,long p,long m){
		 long  result = 1;
		  if(p==0)
		    return 1;
		if (p==1)
		    return n;
		while(p!=0)
		{
		    if(p%2==1)
		        result *= n;
		    if(result>=m)
		    result%=m;
		    p >>=1;
		    n*=n;
		    if(n>=m)
		    n%=m;
		}
		return result;
	    }
	    
	    public static long pow(long n,long p){
		long  result = 1;
		  if(p==0)
		    return 1;
		if (p==1)
		    return n;
		while(p!=0)
		{
		    if(p%2==1)
		        result *= n;	    
		    p >>=1;
		    n*=n;	    
		}
		return result;
	    }
	    public static void debug(Object... o) {
			System.out.println(Arrays.deepToString(o));
		}
	    void run() throws Exception {
			is = System.in;
			out = new PrintWriter(System.out);
			solve();
			out.flush();
		}
	   
	    public static void main(String[] args) throws Exception {
			new Thread(null, new Runnable() {
				public void run() {
					try {
						new code5().run();
					} catch (Exception e) {
						e.printStackTrace();
					}
				}
			}, "1", 1 << 26).start();

		}
	    private byte[] inbuf = new byte[1024];
		public int lenbuf = 0, ptrbuf = 0;
	 
		private int readByte() {
			if (lenbuf == -1)
				throw new InputMismatchException();
			if (ptrbuf >= lenbuf) {
				ptrbuf = 0;
				try {
					lenbuf = is.read(inbuf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return -1;
			}
			return inbuf[ptrbuf++];
		}
	 
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
	 
		private int skip() {
			int b;
			while ((b = readByte()) != -1 && isSpaceChar(b));
			return b;
		}
	 
		private double nd() {
			return Double.parseDouble(ns());
		}
	 
		private char nc() {
			return (char) skip();
		}
	 
		private String ns() {
			int b = skip();
			StringBuilder sb = new StringBuilder();
			while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
	 
		private char[] ns(int n) {
			char[] buf = new char[n];
			int b = skip(), p = 0;
			while (p < n && !(isSpaceChar(b))) {
				buf[p++] = (char) b;
				b = readByte();
			}
			return n == p ? buf : Arrays.copyOf(buf, p);
		}
	 
		private char[][] nm(int n, int m) {
			char[][] map = new char[n][];
			for (int i = 0; i < n; i++)
				map[i] = ns(m);
			return map;
		}
	 
		private int[] na(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = ni();
			return a;
		}
	 
		private int ni() {
			int num = 0, b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}
	 
			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}
	 
		private long nl() {
			long num = 0;
			int b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}
	 
			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}
	 
}