Sliding GCD

Problem Statement

For the set S of natural numbers, let f (S) be the number of elements in the set \\ {GCD (T) | T ⊆ S, T is not empty \\}.

Here, GCD (T) is the greatest integer that divides all the numbers contained in T.
In particular, note that GCD (\\ {a \\}) = a when T consists of only one integer a.

Find f (\\ {i, i + 1, ..., i + W --1 \\}) for i = 1, 2, ..., N --W + 1.

Constraints

* 1 ≤ W ≤ N ≤ 10 ^ 5

Input

Input follows the following format. All given numbers are integers.


N W

Output

The value of f (\\ {i, i + 1, ..., i + W-1 \\}) when i = 1, 2, ..., N-W + 1 is separated by a space. Print on a line.

Examples

Input

10 2


Output

2 3 3 3 3 3 3 3 3


Input

30 7


Output

7 8 9 10 10 11 11 11 11 12 11 12 10 12 12 11 10 12 12 12 10 11 11 13
#define _GLIBCXX_DEBUG
#include <iostream>
#include <vector>
using namespace std;

int main(){
  int N, W;
  cin >> N >> W;
  vector<int> ans(2*(N), 0);
  ans[0] = W;
  for(int i = 1; i <= W/2; ++i){
    ++ans[i+1];
  }
  for(int i = W/2+1; i < W; ++i){
    for(int j = 3; j*i <= N; ++j){
      ++ans[j*i-W+1];
      --ans[j*i-W+1+W-i];
    }
  }
  for(int i = 1; i <= N-W+2; ++i){
    ans[i] += ans[i-1];
  }
  cout << ans[1];
  for(int i = 2; i <= N-W+1; ++i) cout << " " << ans[i];
  cout << endl;
  return 0;
}

