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 <map>
using namespace std;
#define mod 1000000007
map<int,int> m;
vector<pair<int,int> > g;
long long dp[105][100005];
int main()
{
	int n,k;
	scanf("%d%d",&n,&k);
	for (int i=1;i<=n;)
	{
		int f=n/i,r=n/f;
		g.push_back({i,r});
		m[r]=g.size();
		dp[1][g.size()]=dp[1][g.size()-1]+r-i+1;
		i=r+1;
	}
	for (int i=2;i<=k;i++)
	{
		for (int j=1;j<=g.size();j++)
		dp[i][j]=(dp[i][j-1]+dp[i-1][m[n/g[j-1].first]]*(g[j-1].second-g[j-1].first+1))%mod;
	}
	printf("%lld",dp[k][g.size()]);
}