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;
#define int long long
const int mod=1e9+7;
int n,k,cnt,L[70004],R[70004],dp[102][70004];
signed main()
{
	cin>>n>>k;
	int x=1,xu,jia;
	while(x<=n)
	{
		jia=n/x,xu=n/jia;
		L[++cnt]=x,R[cnt]=xu;
		x=xu+1;
	}
	for(int i=1;i<=cnt;i++)dp[1][i]=R[i];
	for(int i=2;i<=k;i++)
	{
		for(int j=1;j<=cnt;j++)dp[i][j]=dp[i-1][cnt-j+1]*(R[j]-L[j]+1)%mod;
		for(int j=1;j<=cnt;j++)(dp[i][j]+=dp[i][j-1])%=mod;
	}
	cout<<dp[k][cnt];
	return 0;
}
/*
dp[i][j]±íÊ¾µÚiÎ»ÓÃÁËÇ°j¶ÎµÄÊý×ÖµÄ·½°¸Êý
dp[i][j]=dp[i-1][cnt-j+1]*(R[j]-L[j]+1)ÓÃµÚj¶Î
dp[i][j]+=dp[i][j-1]ÓÃÇ°j¶Î 
*/