Problem Description

HXY has a sudden inspiration. She wants to find a sequence of positive integers that are all less than or equal to \( n \), with a length of \( p \), and where each number except the first one is a multiple of the previous number. She quickly finds such a sequence. However, she feels it's not enough and wants to know how many such sequences exist. She is overwhelmed by the large data range. Now, she turns to you for help. Please assist her in solving this problem. (Since the result might be very large, output the result modulo \( 10^9 + 7 \).)

Input Format

The first line contains two positive integers \( n \) and \( p \).

Output Format

A single line containing a positive integer, representing the number of sequences that meet the conditions, modulo \( 10^9 + 7 \).

Sample Input and Output

Sample Input #1

3 2

Sample Output #1

5

Sample Input #2

6 4

Sample Output #2

39

Notes

Data Range:

• For 10% of the data, \( p = 1 \);
• For 30% of the data, \( 1 \leq n, p \leq 10 \);
• For 60% of the data, \( 1 \leq n, p \leq 5 \times 10^2 \);
• For 100% of the data, \( 1 \leq n, p \leq 2 \times 10^3 \).

见题面 Input 部分

见题面 Output 部分