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 <bits/stdc++.h>
#define N 32768
#define M 0x3B9ACA07LL
long long a[N]={},b[N],c[N]={},d[N];
#define REP(i,n)for(int i=0;i<n;i++)
int main(){
int n,k; std::cin>>n>>k;
for(int i=1;i<N;i++)a[i]=std::min(i,n),b[i]=n/i;
REP(j,k-1){
for(int i=1;i<N;i++)c[i]=(c[i-1]+b[i])%M;
d[N-1]=c[n/(N-1)];
for(int i=N-2;i>=1;i--)d[i]=(d[i+1]+a[i]*(n/i-n/(i+1)))%M;
std::swap(a,c);
std::swap(b,d);
}
std::cout<<b[1];
}