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>
#define ll long long
using namespace std;
const int MOD=1e9+7;
int n,k,tot;
ll dp[110][100010];
pair<ll,ll> num[1000010];
int main(){
//	freopen("tst.txt","r",stdin);freopen("mans.txt","w",stdout);
	scanf("%d %d",&n,&k);
	for(int x=1,y,tmp;x<=n;){
		tmp=n/x;
		y=n/tmp;
		num[++tot]=make_pair(x,y);
		x=y+1;
	}
	for(int i=1;i<=tot;i++){
		dp[1][i]=num[i].second-num[i].first+1;
		dp[1][i]+=dp[1][i-1];
	}
	for(int i=2;i<=k;i++){
		for(int j=1;j<=tot;j++){
			ll tmp=1LL*dp[i-1][tot-j+1]*(num[j].second-num[j].first+1);
			tmp%=MOD;
			dp[i][j]=dp[i][j-1]+tmp;
			dp[i][j]%=MOD;
		}
	}
	printf("%d",dp[k][tot]%MOD);
	return 0;
}