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 F for(i=1;i<N;i++)
long long M=0x3B9ACA07LL,a[N]={},b[N],c[N]={},n,k,i;
int main(){std::cin>>n>>k;F a[i]=i<n?i:n,b[i]=n/i;while(--k){F c[i]=(c[i-1]+b[i])%M;b[N-1]=c[n/(N-1)];for(i=N-2;i>0;i--)b[i]=(b[i+1]+a[i]*(n/i-n/(i+1)))%M;std::swap(a,c);}std::cout<<b[1];}