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 Practice {
					private static InputStream stream;
					private static byte[] buf = new byte[1024];
					private static int curChar;
					private static int numChars;
					private static SpaceCharFilter filter;
					private static PrintWriter pw;
					private static long mod=1000000009;
				
				    public static void main(String[] args) {
				    	InputReader(System.in);
						pw = new PrintWriter(System.out); 
				        new Thread(null ,new Runnable(){
				           public void run(){
				               try{
				                   solve();//This is solution method
				                   pw.close();
				               } catch(Exception e){
				                   e.printStackTrace();
				               }
				           }
				       },"1",1<<26).start();
				   }
				    
				    
				    
				    private static void solve() throws NumberFormatException, IOException{
				    	

				    	int n=nextInt();
				    	int k=nextInt();
				    	
				    	if(n/2==k){
				    		for(int i=1;i<=n;i++){
				    			pw.print(i+" ");
				    		}
				    	}else if(n/2 > k || n==1){
				    		pw.println(-1);
				    	}else{
				    		int req_start = k-(n-2)/2;
				    	pw.print(req_start+" "+2*req_start+" ");
				    	int req=n-2;
				    	for(int i=1;;i+=2){
				    		if(i!=req_start && i!=2*req_start){
				    			if(i+1==req_start || (i+1)==2*req_start)
				    			continue;
				    			if(req<=0)
			    					break;
				    				pw.print(i+" ");
				    			req--;
				    				if(req<=0)
				    					break;
				    				pw.print((i+1)+" ");
				    				req--;
				    		}
				    		if(req<=0)
				    			break;
				    	}
				    	}
				    	
				    	pw.close();
				}
				   
				    
				    
				    private static BigInteger ncr(int n,int k){
				    	if (k < 0 || k > n) return BigInteger.ZERO;
				        if (n-k < k) k = n-k;
			
				        BigInteger x = BigInteger.ONE;
				        for (int i = 1; i <= k; i++) {
				            x = x.multiply(new BigInteger(""+(n-i+1)));
				            x = x.divide(new BigInteger(""+i));
				        }
			
				return x;
				    }
				    static long fact[];
				private static void factmod(int n,int mod){
					fact=new long[n+1];
					fact[0]=1;
					for(int i=1;i<=n;i++){
						fact[i]=i*fact[i-1];
						//fact[i]%=mod;
				
					}
					
				}
				private static long phi(long n){
					long ans=n;
					if(n%2==0)
						ans-=(ans/2);
					while(n%2==0)
					{
						n/=2;
						
					}
					for(int i=3;i*i<=n;i+=2){
						if(n%i==0){
						while(n%i==0){
							n/=i;
						}
						ans-=(ans/i);
						}
					}
					if(n>2)
						ans-=(ans/n);
					
					return ans;
				}
				static long d,x,y;
				static long modInverse(long A, long M)
				{
				extendedEuclid(A,M);
				return (x%M+M)%M;    //x may be negative
				}
				static 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;
				}
				}
				static boolean prime[];
				public static void sieve(int n){
					prime=new boolean[n+1];
				
					
				}
				public static boolean isPrime(long n) {
					
					if (n <= 1)
						return false;
					if (n <= 3)
						return true;
				
					if (n % 2 == 0 || n % 3 == 0)
						return false;
				
					for (long i = 5; i * i <= n; i = i + 6)
						if (n % i == 0 || n % (i + 2) == 0)
							return false;
				
					return true;
				}
				
				    public static long pow(long n, long p,long mod) {
						if(p==0)
							return 1;
						if(p==1)
							return n%mod;
						if(p%2==0){
							long temp=pow(n, p/2,mod);
						return (temp*temp)%mod;
						}else{
							 	long temp=pow(n,p/2,mod);
							 	temp=(temp*temp)%mod;
							 	return(temp*n)%mod;
							 	
						}
					}
					public static long gcd(long x, long y) {
						if (x == 0)
							return y;
						else
							return gcd( y % x,x);
					}
					
					
					public static void InputReader(InputStream stream1) {
						stream = stream1;
					}
				 
					private static boolean isWhitespace(int c) {
						return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
					}
				 
					private static boolean isEndOfLine(int c) {
						return c == '\n' || c == '\r' || c == -1;
					}
				 
					private static int read() {
						if (numChars == -1)
							throw new InputMismatchException();
						if (curChar >= numChars) {
							curChar = 0;
							try {
								numChars = stream.read(buf);
							} catch (IOException e) {
								throw new InputMismatchException();
							}
							if (numChars <= 0)
								return -1;
						}
						return buf[curChar++];
					}
				 
					private static int nextInt() {
						int c = read();
						while (isSpaceChar(c))
							c = read();
						int sgn = 1;
						if (c == '-') {
							sgn = -1;
							c = read();
						}
						int res = 0;
						do {
							if (c < '0' || c > '9')
								throw new InputMismatchException();
							res *= 10;
							res += c - '0';
							c = read();
						} while (!isSpaceChar(c));
						return res * sgn;
					}
				 
					private static long nextLong() {
						int c = read();
						while (isSpaceChar(c))
							c = read();
						int sgn = 1;
						if (c == '-') {
							sgn = -1;
							c = read();
						}
						long res = 0;
						do {
							if (c < '0' || c > '9')
								throw new InputMismatchException();
							res *= 10;
							res += c - '0';
							c = read();
						} while (!isSpaceChar(c));
						return res * sgn;
					}
				 
					private static String nextToken() {
						int c = read();
						while (isSpaceChar(c))
							c = read();
						StringBuilder res = new StringBuilder();
						do {
							res.appendCodePoint(c);
							c = read();
						} while (!isSpaceChar(c));
						return res.toString();
					}
				 
					private static String nextLine() {
						int c = read();
						while (isSpaceChar(c))
							c = read();
						StringBuilder res = new StringBuilder();
						do {
							res.appendCodePoint(c);
							c = read();
						} while (!isEndOfLine(c));
						return res.toString();
					}
				 
					private static int[] nextIntArray(int n) {
						int[] arr = new int[n];
						for (int i = 0; i < n; i++) {
							arr[i] = nextInt();
						}
						return arr;
					}
				 
					private static int[][] next2dArray(int n, int m) {
						int[][] arr = new int[n][m];
						for (int i = 0; i < n; i++) {
							for (int j = 0; j < m; j++) {
								arr[i][j] = nextInt();
							}
						}
						return arr;
					}
					private static char[][] nextCharArray(int n,int m){
						char [][]c=new char[n][m];
						for(int i=0;i<n;i++){
							String s=nextLine();
							for(int j=0;j<s.length();j++){
								c[i][j]=s.charAt(j);
							}
						}
						return c;
					}
				 
					private static long[] nextLongArray(int n) {
						long[] arr = new long[n];
						for (int i = 0; i < n; i++) {
							arr[i] = nextLong();
						}
						return arr;
					}
				 
					private static void pArray(int[] arr) {
						for (int i = 0; i < arr.length; i++) {
							pw.print(arr[i] + " ");
						}
						pw.println();
						return;
					}
				 
					private static void pArray(long[] arr) {
						for (int i = 0; i < arr.length; i++) {
							pw.print(arr[i] + " ");
						}
						pw.println();
						return;
					}
				 
					private static void pArray(boolean[] arr) {
						for (int i = 0; i < arr.length; i++) {
							pw.print(arr[i] + " ");
						}
						pw.println();
						return;
					}
				 
					private static boolean isSpaceChar(int c) {
						if (filter != null)
							return filter.isSpaceChar(c);
						return isWhitespace(c);
					}
				 
					private interface SpaceCharFilter {
						public boolean isSpaceChar(int ch);
					}
				
					
				}	
				
				class Pair implements Comparable<Pair>{
					
					int city,pop;
					Pair(int city,int pop){
						this.city=city;
						this.pop=pop;
					}
					@Override
					public int compareTo(Pair o) {
				return pop-this.pop;
				
					}
					public int hashCode() {
							int hu = (int) (city ^ (city >>> 32));
							int hv = (int) (pop ^ (pop >>> 32));
							//int hw = (int) (mass ^ (mass >>> 32));
							return 31 * hu + hv ;
						//return 0;
						}
						public boolean equals(Object o) {
							Pair other = (Pair) o;
							return city == other.city && pop == other.pop;
						}
				}