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<iostream>
#include<vector>
#include<algorithm>
using namespace std;

const long long MOD=1e9+7;

long long dp[110][100010];

int main()
{
	int n,k;
	cin>>n>>k;
	vector<int>a;
	for(int i=1;i<=n;)
	{
		a.emplace_back(n/i);
		i=n/(n/i)+1;
	}
	int m=a.size();
	sort(a.begin(),a.end());
	for(int i=0;i<=m;i++)
		dp[1][i]=a[i];
	long long ans=0;
	for(int i=2;i<=k;i++)
	{
		for(int j=0;j<=m;j++)
		{
			int oj=m-j-1;
			int t=a[j]-(j==0?0:a[j-1]);
			dp[i][j]=1ll*t*dp[i-1][oj]%MOD;
			if(i==k)
				ans=(ans+dp[i][j])%MOD;
		}
		for(int j=1;j<=m;++ j)
			dp[i][j]=(dp[i][j]+dp[i][j-1])%MOD;
	}
	printf("%lld\n",ans);
	return 0;
}