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 M 100005
#define P 1000000007
struct hh {
	int l,r;
} num[M];
int dp[105][M];
int main() {
	int n,k,pr=1,cnt=0;
	scanf("%d%d",&n,&k);
	while(pr<=n) {
		int t=n/pr,m=n/t;
		num[++cnt].l=pr;
		num[cnt].r=m;
		pr=m+1;
	}
	for(int i=1;i<=cnt;++i)dp[1][i]=num[i].r-num[i].l+1,dp[1][i]+=dp[1][i-1];
	for(int i=2;i<=k;++i){
		for(int j=1;j<=cnt;++j)
			dp[i][j]=1ll*(num[j].r-num[j].l+1)*dp[i-1][cnt-j+1]%P;
		for(int j=2;j<=cnt;++j)dp[i][j]=(dp[i][j]+dp[i][j-1])%P;
	}
	printf("%d",dp[k][cnt]);
}