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;
typedef long long ll;
const ll md=1e9+7;
ll a[110][100100],b[110][100100];

int main(){
	int n,k;
	scanf("%d%d",&n,&k);
	int ub=100100;
	for(int i=1;i<ub;i++){
		a[1][i]=min(i,n);
		b[1][i]=n/i;
	}
	for(int i=2;i<=k;i++){
		a[i][0]=0;
		for(int j=1;j<ub;j++){
			a[i][j]=(a[i][j-1]+b[i-1][j])%md;
		}
		b[i][ub-1]=a[i][n/(ub-1)];
		for(int j=ub-2;j>=1;j--){
			b[i][j]=(b[i][j+1]+a[i-1][j]*(n/j-n/(j+1)))%md;
		}
	}
	printf("%lld\n",b[k][1]);
	return 0;
}