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

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
const int p=1000000007;
using namespace std;
struct node{
	int a,b;
};
int n,k,dp[102][64000],sum[102][64000];
vector<node>num;
int main(){
	scanf("%d%d",&n,&k);
	int x=1;num.push_back((node)<%0,0%>);
	while(x<=n){
		int t=n/x,y=n/t;
		num.push_back((node)<%x,y%>);
		x=y+1;
	}
	int v=num.size();
	for(int i=1;i<v;i++){
		dp[1][i]=num[i].b-num[i].a+1;
		sum[1][i]=(sum[1][i-1]+dp[1][i])%p;
	}
	for(int i=2;i<=k;i++){
		for(int j=1;j<v;j++){
			dp[i][j]=1ll*sum[i-1][v-j]*(num[j].b-num[j].a+1)%p;
			sum[i][j]=(sum[i][j-1]+dp[i][j])%p;
//			printf("sum=%d\n",dp[i][j]);
		}
	}
	printf("%d\n",sum[k][v-1]);
	return 0;
}