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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
struct Scanner {
  bool hasNext = 1;
  bool hasRead = 1;
  int nextInt() {
    hasRead = 0;
    int res = 0;
    char flag = 1, ch = getchar();
    while (ch != EOF && !isdigit(ch)) {
      hasRead = 1;
      flag = (ch == '-') ? -flag : flag;
      ch = getchar();
    }
    while (ch != EOF && isdigit(ch)) {
      hasRead = 1;
      res = res * 10 + (ch - '0');
      ch = getchar();
    }
    if (ch == EOF) hasNext = 0;
    return res * flag;
  }
  long long nextLL() {
    hasRead = 0;
    long long res = 0;
    char flag = 1, ch = getchar();
    while (ch != EOF && !isdigit(ch)) {
      hasRead = 1;
      flag = (ch == '-') ? -flag : flag;
      ch = getchar();
    }
    while (ch != EOF && isdigit(ch)) {
      hasRead = 1;
      res = res * 10 + (ch - '0');
      ch = getchar();
    }
    if (ch == EOF) hasNext = 0;
    return res * flag;
  }
  char nextChar() {
    hasRead = 0;
    char ch = getchar();
    while (ch != EOF && isspace(ch)) {
      hasRead = 1;
      ch = getchar();
    }
    if (ch == EOF) hasNext = 0;
    return ch;
  }
  int nextString(char *str) {
    hasRead = 0;
    int len = 0;
    char ch = getchar();
    while (ch != EOF && isspace(ch)) {
      hasRead = 1;
      ch = getchar();
    }
    while (ch != EOF && !isspace(ch)) {
      hasRead = 1;
      str[++len] = ch;
      ch = getchar();
    }
    str[len + 1] = 0;
    if (ch == EOF) hasNext = 0;
    return len;
  }
} sc;
long long rd() {
  long long x = sc.nextLL();
  return x;
}
void rd(int &x) { x = sc.nextInt(); }
void rd(long long &x) { x = sc.nextLL(); }
void rd(char &x) { x = sc.nextChar(); }
void rd(char *x) { sc.nextString(x); }
template <typename T1, typename T2>
void rd(pair<T1, T2> &x) {
  rd(x.first);
  rd(x.second);
}
template <typename T>
void rd(T *x, int n) {
  for (int i = 1; i <= n; ++i) rd(x[i]);
}
void printInt(int x) {
  if (x < 0) {
    putchar('-');
    x = -x;
  }
  if (x >= 10) printInt(x / 10);
  putchar('0' + x % 10);
}
void printLL(long long x) {
  if (x < 0) {
    putchar('-');
    x = -x;
  }
  if (x >= 10) printLL(x / 10);
  putchar('0' + x % 10);
}
void pr(int x, char ch = '\n') {
  printInt(x);
  putchar(ch);
}
void pr(long long x, char ch = '\n') {
  printLL(x);
  putchar(ch);
}
template <typename T1, typename T2>
void pr(pair<T1, T2> x, char ch = '\n') {
  pr(x.first, ' ');
  pr(x.second, ch);
}
template <typename T>
void pr(T *x, int n) {
  for (int i = 1; i <= n; ++i) pr(x[i], " \n"[i == n]);
}
template <typename T>
void pr(vector<T> &x) {
  int n = x.size();
  for (int i = 1; i <= n; ++i) pr(x[i - 1], " \n"[i == n]);
}
template <typename T>
void cmin(T &x, T y) {
  if (y < x) x = y;
}
template <typename T>
void cmax(T &x, T y) {
  if (y > x) x = y;
}
const int INF = 0x3f3f3f3f;
const long long LINF = 0x3f3f3f3f3f3f3f3fLL;
const double PI = acos(-1.0);
const double EPS = 1e-9;
const int MOD = 998244353;
int n, m;
vector<int> ans;
struct Solver {
  void InitOnce() {}
  void Read() {
    rd(n);
    rd(m);
  }
  void Solve() {
    ans.clear();
    long long most = 0;
    for (int i = n - 2; i >= 1; i -= 2) most += i;
    if (m > most) {
      puts("-1");
      return;
    }
    ans.push_back(1);
    if (n >= 2) ans.push_back(2);
    int i = 3;
    int cur = 2;
    while (m >= (cur + 1) / 2) {
      ans.push_back(i);
      ++i;
      m -= cur / 2;
      ++cur;
    }
    if (m) {
      while (m < cur / 2) {
        ++i;
        --cur;
      }
      ans.push_back(i);
      m -= cur / 2;
    }
    int BIG = 200000;
    int DELTA = 10001;
    while (n > ans.size()) {
      ans.push_back(BIG);
      BIG += DELTA;
    }
    pr(ans);
  }
} solver;
int main() {
  solver.InitOnce();
  int t = 1;
  t = INF;
  while (t--) {
    solver.Read();
    if (!sc.hasRead) break;
    solver.Solve();
    if (!sc.hasNext) break;
  }
  return 0;
}