Problem:
Score : 600 points

Problem Statement

Find the number of sequences of length K consisting of positive integers such that the product of any two adjacent elements is at most N, modulo 10^9+7.

Constraints

1\leq N\leq 10^9

1 2\leq K\leq 100 (fixed at 21:33 JST)

N and K are integers.

Input

Input is given from Standard Input in the following format:

N K

Output

Print the number of sequences, modulo 10^9+7.

Sample Input 1

3 2

Sample Output 1

5

(1,1), (1,2), (1,3), (2,1), and (3,1) satisfy the condition.

Sample Input 2

10 3

Sample Output 2

147

Sample Input 3

314159265 35

Sample Output 3

457397712

Solution in Julia (1.4.0) (judge verdict: Accepted)

M=10^9+7;n,k=readline()|>split.|>x->parse(Int,x);j=isqrt(n);let x=c=[(i->n÷i-n÷(i+1)).(1:n÷(j+1));fill(1,j)];print((i->x=cumsum(reverse(x)).*c.%M).(1:k)[k][end])end