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>
using namespace std;
#define ll long long
#define M (1000000007)
#define N (10010)
struct data{
	int x,y;
};
int	n,k,cnt,dp[110][64000],sum[64000],sz[64000];
vector<data>q;

int main(){
	scanf("%d%d",&n,&k);
	int x=1;
	while (x<=n){
		int t=n/x;
		int y=n/t;
		q.push_back({x,y});
		sz[++cnt]=y-x+1;
		x=y+1;
	}
	int all=q.size();
	for (int j=1;j<=all;j++) dp[1][j]=sz[j];
	for (int i=2;i<=k;i++){
		for (int j=1;j<=all;j++) sum[j]=(sum[j-1]+dp[i-1][j])%M;
		for (int j=1;j<=all;j++) dp[i][j]=1ll*sum[all-j+1]*sz[j]%M;
	}
	ll ans=0;
	for (int i=1;i<=all;i++) ans=(ans+dp[k][i])%M;
	printf("%lld",ans);
	
}