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.awt.geom.Line2D;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.StreamCorruptedException;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashSet;
import java.util.Hashtable;
import java.util.InputMismatchException;
import java.util.Scanner;
import java.util.Stack;
import java.util.TreeSet;


public class Solution1 
{
    public static void main(String[] args) {
        //      FasterScanner in=new FasterScanner();
        //      PrintWriter out=new PrintWriter(System.out);
        //      int t=in.nextInt();
        //      for(int ii=0;ii<t;ii++)
        //      {
        new Solution1().solve();
        //      }//System.out.println(Long.MIN_VALUE);
        //      out.close();
        //System.out.println(func("anand patel","abjh"));
    }
    public Solution1()
    {
        in=new FasterScanner();
        out=new PrintWriter(System.out);
    }

    public Solution1(FasterScanner in,PrintWriter out)
    {
        this.in=in;
        this.out=out;
    }

    FasterScanner in;
    PrintWriter out;
    //  segmentTree t;
    //  segmentTree c;
    //  long mod=1000000007L ;
    //  long[] arr;
    //  Hashtable<Long, Integer> table;
    //  int d;
    //  int[] count;
    //  int n;
    public void solve()
    {
    //  System.out.println((int)1e9+1);
        boolean[] arr=new boolean[(int)1e6+1];
        ArrayList<Integer> list=new ArrayList<Integer>();
        for(int i=2;i<Math.sqrt(arr.length)+2;i++)
        {
            if(!arr[i])
            {
                for(int j=i*i;j<arr.length;j+=i)
                {
                    arr[j]=true;
                }
            }
        }
        for(int i=2;i<arr.length;i++){
            if(!arr[i]){
                list.add(i);
            }
        }
        //System.out.println(list.get(list.size()-50000));
        int[] arr1=new int[50000+1];
        int[] arr2=new int[50000+1];
        
        for(int i=0;i<arr1.length;i++)
        {
            arr1[i]=list.get(list.size()-i-1);
            arr2[i]=list.get(list.size()-i-1)/2;
        }
        
        int n=in.nextInt();
        int k=in.nextInt();
        if(n==1)
        {
            if(k==0)
            {
                System.out.println(1);
            }
            else
            {
                System.out.println(-1);
            }
            return;
        }
        boolean b=false;
        if(n%2==1)
            b=true;
        n=n/2;
         k=k-(n-1);
        if(k<=0)
        {
            System.out.println(-1);
            return;
        }
        out.print(k+" "+(2*k)+" ");
        int c=2*k+1;
        for(int i=0;i<n-1;i++)
        {
            out.print((c++)+" "+(c++)+" ");
        }
        
        
        if(b)
            out.println(1000000000);
        out.close();
    }

  
    
    public class ss implements Comparable<ss>
    {
        
        long w;
        int r;
        public ss(long w,int r)
        {
            
            this.w=w;
            this.r=r;
        }
        @Override
        public int compareTo(ss o) {
            // TODO Auto-generated method stub
            if(this.w!=o.w)
            {
                return Long.compare(this.w, o.w);
            }

            return 0;
        }

    }


    //source http://codeforces.com/blog/entry/18051
    class segmentTree
    {
        int n;  // array size
        long t[];

        public segmentTree(long[] arr)
        {
            n=arr.length;
            t=new long[3*n];
            for(int i=0;i<n;i++)
            {
                t[n+i]=arr[i];
            }
            build();
        }

        public void print()
        {
            for(int i=n;i<=n+15;i++)
            {
                out.print(t[i]+" ");
            }
            out.println();
        }

        void build() {  // build the tree
            for (int i = n - 1; i > 0; --i) t[i] = Math.max(t[i<<1] , t[i<<1|1]);
        }

        void modify(int p, long value) {  // set value at position p
            for (t[p += n] = value; p > 1; p >>= 1) t[p>>1] = Math.max(t[p] , t[p^1]);
        }

        long query(int l, int r) {  // sum on interval [l, r)
            long res = 0;
            for (l += n, r += n; l < r; l >>= 1, r >>= 1) {
                if ((l&1)!=0) res = Math.max(res,t[l++]);
                if ((r&1)!=0) res = Math.max(t[--r],res);
            }
            return res;
        }
    }

    public class Node
    {
        int start;
        int stop;
        int val;
        Node left;
        Node right;

        int lazy;

        public Node(int start,int stop,int[] arr)
        {
            this.start=start;
            this.stop=stop;
            if(this.start==this.stop)
            {
                //TODO
                this.val=arr[start];
            }
            else
            {
                left=new Node(start,(start+stop)/2,arr);
                right=new Node((start+stop)/2+1,stop,arr);
                //TODO
                this.val=left.val+right.val;
            }
        }

        //      public void update(int idx,int v)
        //      {
        //          if(this.start==this.stop)
        //          {
        //              if(this.start==idx)
        //              {
        //                  this.val+=v;
        //              }
        //          }
        //          else
        //          {
        //              if(this.start<=idx && this.stop>=idx)
        //              {
        //                  left.update(idx, v);
        //                  right.update(idx, v);
        //                  this.val=left.val+right.val;
        //              }
        //          }
        //      }

        public int lazyUpdate(int l,int r)
        {
            if(l>r)
            {
                return 0;
            }
            if(this.start==this.stop)
            {
                if(l<=this.start && this.start<=r)
                {
                    this.val^=1;
                    return this.val;
                }
                else
                {
                    return this.val;
                }
            }
            else if(this.start>r || this.stop<l)
            {
                return this.val;
            }
            else if(this.start>=l && this.stop<=r)
            {
                this.lazy=1-this.lazy;
                this.val=this.stop-this.start+1-this.val;
                return this.val;
            }
            else
            {
                if(this.lazy==0)
                {
                    //left.query(l, r)+right.query(l, r);
                    this.val=left.lazyUpdate(l, r);
                    this.val+=right.lazyUpdate(l, r);
                }
                else
                {
                    this.lazy=0;
                    left.lazyUpdate(start,stop);
                    right.lazyUpdate(start, stop);
                    this.val=left.lazyUpdate(l, r);
                    this.val+=right.lazyUpdate(l, r);
                }
                return this.val;
            }
        }

        public int query(int l,int r)
        {
            if(l>r)
            {
                return 0;
            }
            if(this.start==this.stop)
            {
                if(l<=this.start && this.start<=r)
                {
                    return this.val;
                }
                else
                {
                    return 0;
                }
            }
            else if(this.start>r || this.stop<l)
            {
                return 0;
            }
            else if(this.start>=l && this.stop<=r)
            {
                return this.val;
            }
            else
            {
                if(this.lazy==0)
                {
                    return left.query(l, r)+right.query(l, r);
                }
                else
                {
                    this.lazy=0;
                    this.val=left.lazyUpdate(start,stop);
                    this.val+=right.lazyUpdate(start, stop);
                    return left.query(l, r)+right.query(l, r);
                }
            }
        }
    }


    public class UF {

        private int[] parent;  // parent[i] = parent of i
        private byte[] rank;   // rank[i] = rank of subtree rooted at i (never more than 31)
        private int count;   
        int[] seg;
        int max;
        // number of components
        public UF(int N) {
            if (N < 0) throw new IllegalArgumentException();
            count = N;
            parent = new int[N];
            rank = new byte[N];
            seg=new int[N];
            for (int i = 0; i < N; i++) {
                parent[i] = i;
                rank[i] = 0;
                seg[i]=1;
            }
            max=1;
        }

        public int find(int p) {
            if (p < 0 || p >= parent.length) throw new IndexOutOfBoundsException();
            while (p != parent[p]) {
                parent[p] = parent[parent[p]];    // path compression by halving
                p = parent[p];
            }
            return p;
        }

        public int count() {
            return count;
        }

        public boolean connected(int p, int q) {
            return find(p) == find(q);
        }

        public boolean union(int p, int q) {
            //  System.out.println("uf "+p+" "+q);
            int rootP = find(p);
            int rootQ = find(q);
            if (rootP == rootQ) return false;

            // make root of smaller rank point to root of larger rank
            if      (rank[rootP] < rank[rootQ])
            {
                parent[rootP] = rootQ;
                seg[rootQ]+=seg[rootP];
                max=Math.max(seg[rootQ],max);
            }
            else if (rank[rootP] > rank[rootQ])
            {
                parent[rootQ] = rootP;
                seg[rootP]+=seg[rootQ];
                max=Math.max(seg[rootP],max);
            }
            else {
                parent[rootQ] = rootP;
                rank[rootP]++;
                seg[rootP]+=seg[rootQ];
                max=Math.max(seg[rootP],max);
            }
            count--;
            return true;
        }

    }



    long pow(long a,int n,long m)
    {
        if(n==1)
            return a;
        if(n==0)
            return 1;
        long ans=pow(a,n/2,m);
        ans*=ans;
        ans%=m;
        if(n%2!=0)
            ans*=a;
        ans%=m;
        return ans;
    }

    public static int gcd(long a, long b) {
        BigInteger b1 = BigInteger.valueOf(a);
        BigInteger b2 = BigInteger.valueOf(b);
        BigInteger gcd = b1.gcd(b2);
        return gcd.intValue();
    }




    public static class FasterScanner {
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = System.in.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public 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();
        }

        public String nextString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public 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;
        }

        public 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;
        }

        public int[] nextIntArray(int n) {
            int[] arr = new int[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextInt();
            }
            return arr;
        }

        public long[] nextLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
    }
}