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>
#include<vector>
#include<algorithm>
using namespace std;

const long long MOD=1e9+7;
int n,k,dp1[1000000];
vector<long long>cnt,dp2;

int main()
{
	cin>>n>>k;
	for(long long s=n;s>0;)
	{
		long long cur_s=n/(n/s+1);
		cnt.push_back(s-cur_s);
		s=cur_s;
	}
	reverse(cnt.begin(),cnt.end());
	int m=cnt.size();
	dp2=cnt;
	for(int i=1;i<k;i++)
	{
		for(int j=0;j<m;j++)
		{
			int t=m-1-j;
			dp1[t]=dp2[j]%MOD;
		}
		for(int j=m-1;j>=0;j--)
		{
			dp1[j]=(dp1[j]+(j+1<m?dp1[j+1]:0))%MOD;
			dp2[j]=(dp1[j]*cnt[j])%MOD;
		}
	}
	long long ans=0;
	for(int i=0;i<dp2.size();i++) 
		ans=(ans+dp2[i])%MOD;
	cout<<ans;
}