#include<bits/stdc++.h>
#define LL long long
#define M 105
#define N 31630
using namespace std;
const int P=1e9+7; 
int dp[M][2*N];
int sum[M][2*N];
void Add(int &x,int y){
	x+=y;
	if(x>=P)x-=P;
}
struct node{
	int x,y;
};
vector<node>num;
int main(){
	int m,n;
	cin>>m>>n;
	int x=1;
	num.push_back((node){0,0});
	while(x<=m){
		int t=m/x;
		int y=m/t;  
		num.push_back((node){x,y}); 
		x=y+1; 
	}  
	int k=num.size()-1;
	for(int i=1;i<=k;i++){
		dp[1][i]=num[i].y-num[i].x+1; 
		dp[1][i]+=dp[1][i-1];
	} 
	for(int i=2;i<=n;i++){ 
		for(int j=1;j<=k;j++){
			dp[i][j]=1LL*dp[i-1][k-j+1]*(num[j].y-num[j].x+1)%P; 
			Add(dp[i][j],dp[i][j-1]);
		}
	}
	int ans=dp[n][k];
	printf("%d\n",ans);
	return 0;
}
### Prompt

In cpp, your task is to solve 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 LL long long
#define M 105
#define N 31630
using namespace std;
const int P=1e9+7; 
int dp[M][2*N];
int sum[M][2*N];
void Add(int &x,int y){
	x+=y;
	if(x>=P)x-=P;
}
struct node{
	int x,y;
};
vector<node>num;
int main(){
	int m,n;
	cin>>m>>n;
	int x=1;
	num.push_back((node){0,0});
	while(x<=m){
		int t=m/x;
		int y=m/t;  
		num.push_back((node){x,y}); 
		x=y+1; 
	}  
	int k=num.size()-1;
	for(int i=1;i<=k;i++){
		dp[1][i]=num[i].y-num[i].x+1; 
		dp[1][i]+=dp[1][i-1];
	} 
	for(int i=2;i<=n;i++){ 
		for(int j=1;j<=k;j++){
			dp[i][j]=1LL*dp[i-1][k-j+1]*(num[j].y-num[j].x+1)%P; 
			Add(dp[i][j],dp[i][j-1]);
		}
	}
	int ans=dp[n][k];
	printf("%d\n",ans);
	return 0;
}
```