#include<bits/stdc++.h>
using namespace std;
long long a,b,c,d,e,dp[102][64000],k,p[64009],pi,pp[64009],ppi,sq,i,j,mod=1000000007,zx[64000];
map <long long, long long> m;
int main(){
	ios_base::sync_with_stdio(false),cin.tie(0),cout.tie(0);
	cin>>a>>k;
	sq=sqrt(a);
	for(b=1; b<=sq; b++){
		c=b;d=a/b;
		pi++;p[pi]=c;
		m[c]=pi;
		if(c!=d){
			ppi++;pp[ppi]=d;
		}
	}
	for(b=ppi; b>=1; b--){
		pi++;p[pi]=pp[b];
		m[pp[b]]=pi;
	}
	for(b=1; b<=pi; b++){
		zx[b]=m[a/p[b]];
	}
	for(i=1; i<=pi; i++) dp[0][i]=1;
	for(i=1; i<=k; i++){
		for(j=1; j<=pi; j++){
			dp[i][j]=dp[i-1][zx[j]];
		}
		for(j=1; j<=pi; j++){
			dp[i][j]=dp[i][j-1]+dp[i][j]*(p[j]-p[j-1]);
			dp[i][j]%=mod;
		}
	}
	cout<<dp[k][pi];
	return 0;
}
### 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<bits/stdc++.h>
using namespace std;
long long a,b,c,d,e,dp[102][64000],k,p[64009],pi,pp[64009],ppi,sq,i,j,mod=1000000007,zx[64000];
map <long long, long long> m;
int main(){
	ios_base::sync_with_stdio(false),cin.tie(0),cout.tie(0);
	cin>>a>>k;
	sq=sqrt(a);
	for(b=1; b<=sq; b++){
		c=b;d=a/b;
		pi++;p[pi]=c;
		m[c]=pi;
		if(c!=d){
			ppi++;pp[ppi]=d;
		}
	}
	for(b=ppi; b>=1; b--){
		pi++;p[pi]=pp[b];
		m[pp[b]]=pi;
	}
	for(b=1; b<=pi; b++){
		zx[b]=m[a/p[b]];
	}
	for(i=1; i<=pi; i++) dp[0][i]=1;
	for(i=1; i<=k; i++){
		for(j=1; j<=pi; j++){
			dp[i][j]=dp[i-1][zx[j]];
		}
		for(j=1; j<=pi; j++){
			dp[i][j]=dp[i][j-1]+dp[i][j]*(p[j]-p[j-1]);
			dp[i][j]%=mod;
		}
	}
	cout<<dp[k][pi];
	return 0;
}
```