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 mo=1e9+7;
const int N=1e5+10;
int n,k,ans;
int L[N],R[N],val[N],pos[N],cnt,sum[2][N];
int main(){
	scanf("%d%d",&k,&n);
	for (int l=1,r;l<=k;l=r+1){
		r=k/(k/l);
		L[++cnt]=l,R[cnt]=r,val[cnt]=k/l;
	}
	for (int i=1;i<=cnt;i++){
		sum[0][i]=1;
		pos[i]=upper_bound(L+1,L+cnt+1,val[i])-L-1;
	}
	int cur=1;
	for (int i=1;i<=n;i++,cur^=1)
		for (int j=1;j<=cnt;j++) sum[cur][j]=(sum[cur][j-1]+sum[cur^1][pos[j]]*1ll*(R[j]-L[j]+1)%mo)%mo;
	cout<<sum[cur^1][cnt];
	return 0;
}