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

typedef long long LL;
const int MK=105;
const int M=70005; // sqrt(1e9)*2
const int MO=1e9+7;
int cnt[M];
int dp[MK][M];

inline int add(int x,int y)
{
	x+=y;
	if(x>=MO) x-=MO;
	return x;
}
inline int mul(int x,int y)
{
	return 1LL*x*y%MO;
}

int main()
{
	int n,k;
	cin>>n>>k;
	int l,r,m=0;
	for(int i=1;i<=n;)
	{
		l=i;
		r=n/(n/i);
		//cout<<l<<" "<<r<<endl;
		cnt[++m]=(r-l+1);
		i=r+1;
	}
	dp[0][0]=1;
	for(int i=1;i<=k;i++)
	{
		int sum=dp[i-1][0];
		for(int j=m;j>=1;j--)
		{
			sum=add(sum,dp[i-1][m+1-j]);
			dp[i][j]=mul(sum,cnt[j]);
		}
	}
	int ans=0;
	for(int i=1;i<=m;i++)
		ans=add(ans,dp[k][i]);
	cout<<ans<<endl;
	return 0;
}
### Prompt

Create a solution in CPP for 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>
using namespace std;

typedef long long LL;
const int MK=105;
const int M=70005; // sqrt(1e9)*2
const int MO=1e9+7;
int cnt[M];
int dp[MK][M];

inline int add(int x,int y)
{
	x+=y;
	if(x>=MO) x-=MO;
	return x;
}
inline int mul(int x,int y)
{
	return 1LL*x*y%MO;
}

int main()
{
	int n,k;
	cin>>n>>k;
	int l,r,m=0;
	for(int i=1;i<=n;)
	{
		l=i;
		r=n/(n/i);
		//cout<<l<<" "<<r<<endl;
		cnt[++m]=(r-l+1);
		i=r+1;
	}
	dp[0][0]=1;
	for(int i=1;i<=k;i++)
	{
		int sum=dp[i-1][0];
		for(int j=m;j>=1;j--)
		{
			sum=add(sum,dp[i-1][m+1-j]);
			dp[i][j]=mul(sum,cnt[j]);
		}
	}
	int ans=0;
	for(int i=1;i<=m;i++)
		ans=add(ans,dp[k][i]);
	cout<<ans<<endl;
	return 0;
}
```