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;
int n,k,b[100005],l;
long long dp[105][65005];
const int M=1e9+7;
int main(){
	scanf("%d %d",&n,&k);
	int z=1,q;
	while(z<=n){
		q=n/(n/z);
		b[++l]=q-z+1;
		z=q+1;
	}
	n=l;
	for(int i=1;i<=n;++i){
		dp[1][i]=dp[1][i-1]+b[i];
	}
	for(int i=2;i<=k;++i){
		for(int o=1;o<=n;++o){
			dp[i][o]=(1ll*b[o]*dp[i-1][n-o+1]%M)+dp[i][o-1];
			if(dp[i][o]>=M)dp[i][o]-=M;
		}
	}
	printf("%lld",dp[k][n]);
}