Problem: Kuroni is the coordinator of the next Mathforces round written by the "Proof by AC" team. All the preparation has been done, and he is discussing with the team about the score distribution for the round.

The round consists of n problems, numbered from 1 to n. The problems are ordered in increasing order of difficulty, no two problems have the same difficulty. A score distribution for the round can be denoted by an array a_1, a_2, ..., a_n, where a_i is the score of i-th problem. 

Kuroni thinks that the score distribution should satisfy the following requirements:

  * The score of each problem should be a positive integer not exceeding 10^9. 
  * A harder problem should grant a strictly higher score than an easier problem. In other words, 1 ≤ a_1 < a_2 < ... < a_n ≤ 10^9. 
  * The balance of the score distribution, defined as the number of triples (i, j, k) such that 1 ≤ i < j < k ≤ n and a_i + a_j = a_k, should be exactly m. 



Help the team find a score distribution that satisfies Kuroni's requirement. In case such a score distribution does not exist, output -1.

Input

The first and single line contains two integers n and m (1 ≤ n ≤ 5000, 0 ≤ m ≤ 10^9) — the number of problems and the required balance.

Output

If there is no solution, print a single integer -1.

Otherwise, print a line containing n integers a_1, a_2, ..., a_n, representing a score distribution that satisfies all the requirements. If there are multiple answers, print any of them.

Examples

Input


5 3


Output


4 5 9 13 18

Input


8 0


Output


10 11 12 13 14 15 16 17


Input


4 10


Output


-1

Note

In the first example, there are 3 triples (i, j, k) that contribute to the balance of the score distribution. 

  * (1, 2, 3) 
  * (1, 3, 4) 
  * (2, 4, 5) 

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;


public class Main {
    static int inf = (int) (1e9 + 7);
    static int n;
    static ArrayList<Integer> gr[];
    static boolean used[], good[];
    static int cnt_good;


    static void find(int v, int fin) {
        if (v == fin || !good[v]) return;
        good[v] = false;
        cnt_good--;
        for(int i : gr[v]) {
            find(i, fin);
        }
    }

    static void r() {
        for(int i = 0;i < n;i++) used[i] = false;
    }

    static void solve() throws IOException {
        scan();
        cnt_good = n;
        used = new boolean[n];
        good = new boolean[n];
        for(int i = 0;i < n;i++) good[i] = true;

        int it = 0;
        while(cnt_good != 1) {
            for(int v1 = 0;v1 < n;v1++) {
                if (!good[v1]) continue;
                boolean temp = false;
                for(int i : gr[v1]) {
                    int v2 = gr[i].get(0);
                    if ((v2 == v1 || !good[v1]) && gr[i].size() >= 2) v2 = gr[i].get(1);
                    if (cnt_good == 2) v2 = i;
                    if (v2 == v1 || !good[v2]) continue;
                    pw.println("? " + (v1 + 1) + " " + (v2 + 1));
                    pw.flush();
                    int w = sc.nextInt() - 1;

                    find(v1, w);
                    r();
                    find(v2, w);
                    r();
                    temp = true;
                    break;
                 }
                if (temp) break;
            }
            it++;
            if (it > n / 2) n /= 0;
        }

        int res = 0;
        for(int i = 0;i < n;i++) if (good[i]) res = i + 1;
        pw.println("! " + res);
    }

    static void scan() throws IOException {
        n = sc.nextInt();
        gr = new ArrayList[n];
        for(int i = 0;i < n;i++) gr[i] = new ArrayList<>();
        for(int i = 0;i < n - 1;i++) {
            int v1 = sc.nextInt() - 1;
            int v2 = sc.nextInt() - 1;
            gr[v1].add(v2);
            gr[v2].add(v1);
        }
    }


    public static void main(String[] args) throws IOException {
        sc = new Scanner(System.in);
        pw = new PrintWriter(System.out);
        int n = sc.nextInt();
        int m = sc.nextInt();
        ArrayList<Integer> ans = new ArrayList<>();
        int id = 1;
        if (m != 0) {
            while (true) {
                if (ans.size() / 2 > m) break;
                m -= ans.size() / 2;
                ans.add(id);
                id++;
            }
        }
        if (m != 0) {
            int cnt = ans.size();
            while (true) {
                id++;
                cnt--;
                if (cnt / 2 == m) {
                    ans.add(id);
                    m = 0;
                    break;
                }
            }
        }



        int c1 = (int) 1e9;
        int c2 = 20001;

        //if (ans.get(ans.size() - 1) * 2 >= c2) n /= 0;

        while(ans.size() < n) {
            if (c1 * 2 <= 1e9) n /= 0;
            ans.add(c1);
            c1 -= c2;
        }

        Collections.sort(ans);

        if (ans.size() > n) pw.println(-1);
        else {
            for(int i : ans) pw.print(i + " ");
        }

        pw.close();
    }

    static Scanner sc;
    static PrintWriter pw;

    static class Scanner {
        BufferedReader br;
        StringTokenizer st = new StringTokenizer("");

        Scanner(InputStream in) throws FileNotFoundException {
            br = new BufferedReader(new InputStreamReader(in));
        }

        Scanner(String in) throws FileNotFoundException {
            br = new BufferedReader(new FileReader(in));
        }

        String next() throws IOException {
            while (!st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }
    }

}

class pair {
    int a, t;

    pair(int a, int t) {
        this.a = a;
        this.t = t;
    }

    pair() {
    }

}