Problem: 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.

Examples

Input

3 2


Output

5


Input

10 3


Output

147


Input

314159265 35


Output

457397712

Solution (in CPP):

Solution:
#include<iostream>
#define N 32768
long a[N],b[N],c[N]={},n,k,i=N;
int main(){
for(std::cin>>n>>k;--i;a[i]=i<n?i:n)b[i]=n/i;
while(--k){
for(;++i<N;)c[i]=c[i-1]+b[i];
//for(b[--i]=c[n/i];--i;a[i]=c[i])b[i]=(b[i+1]+a[i]*(n/i-n/(i+1)))%0x3B9ACA07;
for(*b=c[n/--i];--i;a[i]=c[i])*b=b[i]=(*b+a[i]*(n/i-n/(i+1)))%0x3B9ACA07;
}
std::cout<<b[1];
}