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
import java.util.Scanner;

public class Main {
	static Scanner sc = new Scanner(System.in);

	public static void main(String[] args) {
		int N = sc.nextInt();
		int W = sc.nextInt();
		int[] a = new int[N * 2 + 1];
		a[1] += W / 2;
		for (int i = W / 2 + 1; i < W; ++i) {
			a[1]++;
			for (int j = i; j <= N; j += i) {
				if (j > i * 2) a[j - W + 1]++;
				a[j + 1]--;
			}
		}
		for (int i = W; i <= N; ++i) {
			a[i - W + 1]++;
			a[i + 1]--;
		}
		StringBuilder sb = new StringBuilder();
		for (int i = 1; i <= N - W + 1; ++i) {
			a[i] += a[i - 1];
			if (i != 1) sb.append(" ");
			sb.append(a[i]);
		}
		System.out.println(sb);
	}
}