#include<bits/stdc++.h>
#define For(a,b,c) for(int a=b;a<=c;++a)
#define Dor(a,b,c) for(int a=b;a>=c;--a)
using namespace std;
const int M=100000,N=102,P=1000000007;
int n,a,b,k,C[M],F[N][M],S[M];
int main() {
	scanf("%d%d",&n,&k),a=b=(int)sqrt(n);
	if(b*b==n) --b;
	For(i,1,b) C[i]=n/i-max(a,n/(i+1));
	For(i,1,a) F[1][i]=1;
	For(i,a+1,a+b) F[1][i]=C[a+b-i+1];
	For(i,2,k) {
		For(j,1,a+b) S[j]=(S[j-1]+F[i-1][j])%P;
		For(j,1,a) F[i][j]=S[a+b-j+1];
		For(j,a+1,a+b) {
			int u=a+b-j+1;
			F[i][j]=1LL*C[u]*S[u]%P;
		}
	}
	int ans=0;
	For(i,1,a+b) ans=(ans+F[k][i])%P;
	printf("%d",ans);
	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<bits/stdc++.h>
#define For(a,b,c) for(int a=b;a<=c;++a)
#define Dor(a,b,c) for(int a=b;a>=c;--a)
using namespace std;
const int M=100000,N=102,P=1000000007;
int n,a,b,k,C[M],F[N][M],S[M];
int main() {
	scanf("%d%d",&n,&k),a=b=(int)sqrt(n);
	if(b*b==n) --b;
	For(i,1,b) C[i]=n/i-max(a,n/(i+1));
	For(i,1,a) F[1][i]=1;
	For(i,a+1,a+b) F[1][i]=C[a+b-i+1];
	For(i,2,k) {
		For(j,1,a+b) S[j]=(S[j-1]+F[i-1][j])%P;
		For(j,1,a) F[i][j]=S[a+b-j+1];
		For(j,a+1,a+b) {
			int u=a+b-j+1;
			F[i][j]=1LL*C[u]*S[u]%P;
		}
	}
	int ans=0;
	For(i,1,a+b) ans=(ans+F[k][i])%P;
	printf("%d",ans);
	return 0;
}
```