Sliding GCD

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

inputFormat

Input

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

N W

outputFormat

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

样例

10 2

2 3 3 3 3 3 3 3 3