#include<bits/stdc++.h>
#define mod 1000000007
using namespace std;
int n,k,add;
int f[100005],cnt,d[100005];
int dp[105][100005];

int main(){
	cin>>n>>k;
	for(int l=1,r;l<=n;l=r+1){
		r=n/(n/l);
		f[++cnt]=n/l;
		d[cnt]=r;
	}
	for(int i=1;i<=cnt;i++) dp[1][i]=d[i]-d[i-1];
	for(int i=2;i<=k;i++){
		int add=0;
		for(int j=cnt;j>=1;j--){
			add+=dp[i-1][cnt-j+1];
			add%=mod;
			dp[i][j]=1LL*(d[j]-d[j-1])*add%mod;
		}
	}
	int ans=0;
	for(int i=1;i<=cnt;i++) ans+=dp[k][i],ans%=mod;
	cout<<ans;
	
	return 0;
}
### Prompt

Your task is to create 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<bits/stdc++.h>
#define mod 1000000007
using namespace std;
int n,k,add;
int f[100005],cnt,d[100005];
int dp[105][100005];

int main(){
	cin>>n>>k;
	for(int l=1,r;l<=n;l=r+1){
		r=n/(n/l);
		f[++cnt]=n/l;
		d[cnt]=r;
	}
	for(int i=1;i<=cnt;i++) dp[1][i]=d[i]-d[i-1];
	for(int i=2;i<=k;i++){
		int add=0;
		for(int j=cnt;j>=1;j--){
			add+=dp[i-1][cnt-j+1];
			add%=mod;
			dp[i][j]=1LL*(d[j]-d[j-1])*add%mod;
		}
	}
	int ans=0;
	for(int i=1;i<=cnt;i++) ans+=dp[k][i],ans%=mod;
	cout<<ans;
	
	return 0;
}
```