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.DataInputStream;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Iterator;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.TreeMap;
public class A { 
	static void merge(int arr[], int l, int m, int r) 
    { 
        int n1 = m - l + 1; 
        int n2 = r - m; 

        int L[] = new int [n1]; 
        int R[] = new int [n2]; 
        for (int i=0; i<n1; ++i) 
            L[i] = arr[l + i]; 
        for (int j=0; j<n2; ++j) 
            R[j] = arr[m + 1+ j]; 
        int i = 0, j = 0; 
        int k = l; 
        while (i < n1 && j < n2) 
        { 
            if (L[i] <= R[j]) 
            { 
                arr[k] = L[i]; 
                i++; 
            } 
            else
            { 
                arr[k] = R[j]; 
                j++; 
            } 
            k++; 
        } 
        while (i < n1) 
        { 
            arr[k] = L[i]; 
            i++; 
            k++; 
        } 
        while (j < n2) 
        { 
            arr[k] = R[j]; 
            j++; 
            k++; 
        } 
    } 
    static void sort(int arr[], int l, int r) 
    { 
        if (l < r) 
        { 
            int m = (l+r)/2; 
            sort(arr, l, m); 
            sort(arr , m+1, r); 
            merge(arr, l, m, r); 
        } 
    }
    static void revOrder(int[] arr) {
    	int[] a = new int[arr.length];
		for(int i=0;i<arr.length;i++) {
			a[i] = arr[arr.length-i-1];
		}
		for(int i=0;i<arr.length;i++) arr[i] = a[i];
	}
    static int gcd(int a, int b) {
    	if(a==0) return b;
    	return gcd(b%a, a);
    }

	public static void main(String[] args) {
		try {
			BufferInput in = new BufferInput();
			StringBuilder sb = new StringBuilder();
			int n = in.nextInt();
			int k = in.nextInt();
			if(n==1) {
				if(k==0) System.out.println("1");
				else System.out.println("-1");
				return;
			}
			if(k<n/2) {
				System.out.println("-1");
				return;
			}
			int[] res = new int[n];
			int i = 0;
			int x = 1;
			int last = n/2;
			last*=2;
			int l = last;
			HashMap<Integer, Integer> map = new HashMap<>();
			for(i=0;i<n;i++) {
				res[i] = i+1;
				map.put(i+1, 1);
			}
			k-=l/2;
			if(k<0) {
				System.out.println("-1");
				return;
			}
			if(k!=0) {
				k++;
				map.remove(res[l-2]);
				map.remove(res[l-1]);
				int j = k;
				while(k<res[l-2]) k+=j;
				res[l-2] = k;
				map.put(k, 1);
				while(map.containsKey(k)) k+=j;
				res[l-1] = k;
				if(last!=n) {
					res[n-1] = (int) 1e9;
				}
			}
//			int sum = 0;
//			for(i=0;i<n;i+=2) {
//				if(i+1<n) sum+=gcd(res[i], res[i+1]);
//			}
//			System.out.println(sum);
			
//			if(k<l)
//			while(i<last&&k<l) {
//				res[i]=x;
//				res[i+1]=x+1;
//				map.put(x, 1);
//				map.put(x+1, 1);
//				x+=2;
//				i+=2;
//				k--;
//				l-=2;
//			}
//			else {
//				while(i<last&&l>2) {
//					res[i]=x;
//					res[i+1]=x+1;
//					map.put(x, 1);
//					map.put(x+1, 1);
//					x+=2;
//					i+=2;
//					k--;
//					l-=2;
//				}
//			}
//			if(i<last) {
//			x=k;
//			int f = 0;
//			while(x<(int)1e9&&map.containsKey(x)) {
//				x+=k;
//			}
//			if(x>=1e9) {
//				System.out.println("-1");
//				return;
//			}
//			int j =2;
//			int v = x*2;
//			while(v<(int)1e9&&map.containsKey(v)) {
//				j++;
//				v = j*i;
//			}
//			if(v>=1e9) {
//				System.out.println("-1");
//				return;
//			}
//			res[i] = x;
//			res[i+1] = v;
//			}
//			if(last!=n) {
//				res[n-1] = (int) 1e9;
//			}
			for(i=0;i<n;i++) sb.append(res[i]+" ");
			System.out.println(sb);
			
		}catch(Exception e) {}

	}
static class BufferInput {
		
		final private int BUFFER_SIZE = 1 << 16;
		
		private DataInputStream din;
		
		private byte[] buffer;
		
		private int bufferPointer, bytesRead;
		
		public BufferInput() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public BufferInput(String file_name) throws IOException {
			din = new DataInputStream(new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public String readLine() throws IOException {
			byte[] buf = new byte[64];
			int cnt = 0, c;
			while ((c = read()) != -1) {
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String(buf, 0, cnt);
		}
		
		public String nextString() throws IOException{
			
			byte c = read();
			while(Character.isWhitespace(c)){
				c = read();
			}
			
			StringBuilder builder = new StringBuilder();
			builder.append((char)c);
			c = read();
			while(!Character.isWhitespace(c)){
				builder.append((char)c);
				c = read();
			}
			
			return builder.toString();
		}
		
		public int nextInt() throws IOException {
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (neg)
				return -ret;
			return ret;
		}
		
		public int[] nextIntArray(int n) throws IOException {
			int arr[] = new int[n];
			for(int i = 0; i < n; i++){
				arr[i] = nextInt();
			}
			return arr;
		}
		public long nextLong() throws IOException {
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}
		
		public long[] nextLongArray(int n) throws IOException {
			long arr[] = new long[n];
			for(int i = 0; i < n; i++){
				arr[i] = nextLong();
			}
			return arr;
		}
		
		public char nextChar() throws IOException{
			byte c = read();
			while(Character.isWhitespace(c)){
				c = read();
			}
			return (char) c;	
		}
		public double nextDouble() throws IOException {
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();

			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (c == '.') {
				while ((c = read()) >= '0' && c <= '9') {
					ret += (c - '0') / (div *= 10);
				}
			}

			if (neg)
				return -ret;
			return ret;
		}
		public double[] nextDoubleArray(int n) throws IOException {
			double arr[] = new double[n];
			for(int i = 0; i < n; i++){
				arr[i] = nextDouble();
			}
			return arr;
		}
		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}
		private byte read() throws IOException {
			if (bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}

		public void close() throws IOException {
			if (din == null)
				return;
			din.close();
		}
	}
}