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;
const int P=1e9+7;
int n,k,m;
int dp[101][64000],sum[101][64000];
struct node {
	int a,b;
};
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;
	}
	m=num.size();
	for(int i=1; i<m; 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<m; j++) {
			dp[i][j]=1ll*sum[i-1][m-j]*(num[j].b-num[j].a+1)%P;
			sum[i][j]=(sum[i][j-1]+dp[i][j])%P;
		}
	}
	printf("%d",sum[k][m-1]);
}