#include<iostream>
#include<algorithm>
#include<vector>
using namespace std;
int K;
long N,mod=1e9+7;
int L[2<<17],R[2<<17];
long dp[101][2<<17];
int main()
{
	cin>>N>>K;
	int id=0;
	for(int i=1;i*i<=N;i++)
	{
		L[id]=R[id]=i;
		id++;
	}
	int T=L[id-1];
	if(T*T==N)T--;
	for(;T>=1;T--)
	{
		L[id]=R[id-1]+1;
		R[id]=N/T;
		id++;
	}
	for(int i=0;i<id;i++)dp[0][i]=R[i]-L[i]+1;
	for(int i=0;i<K-1;i++)
	{
		for(int j=1;j<id;j++)dp[i][j]=(dp[i][j]+dp[i][j-1])%mod;
		for(int j=0;j<id;j++)
		{
			dp[i+1][j]=(dp[i+1][j]+dp[i][id-j-1]*(R[j]-L[j]+1)%mod)%mod;
		}
	}
	long ans=0;
	for(int j=0;j<id;j++)ans=(ans+dp[K-1][j])%mod;
	cout<<ans<<endl;
}

### Prompt

Your challenge is to write a Cpp solution to the following 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

### Response

```cpp
#include<iostream>
#include<algorithm>
#include<vector>
using namespace std;
int K;
long N,mod=1e9+7;
int L[2<<17],R[2<<17];
long dp[101][2<<17];
int main()
{
	cin>>N>>K;
	int id=0;
	for(int i=1;i*i<=N;i++)
	{
		L[id]=R[id]=i;
		id++;
	}
	int T=L[id-1];
	if(T*T==N)T--;
	for(;T>=1;T--)
	{
		L[id]=R[id-1]+1;
		R[id]=N/T;
		id++;
	}
	for(int i=0;i<id;i++)dp[0][i]=R[i]-L[i]+1;
	for(int i=0;i<K-1;i++)
	{
		for(int j=1;j<id;j++)dp[i][j]=(dp[i][j]+dp[i][j-1])%mod;
		for(int j=0;j<id;j++)
		{
			dp[i+1][j]=(dp[i+1][j]+dp[i][id-j-1]*(R[j]-L[j]+1)%mod)%mod;
		}
	}
	long ans=0;
	for(int j=0;j<id;j++)ans=(ans+dp[K-1][j])%mod;
	cout<<ans<<endl;
}

```