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 int N = 100000 + 10;
const int mod = 1e9 + 7;
ll a[110][N],id[N],di[N];
map<int,int> m;
int main(){
    int n,k; cin>>n>>k;
    int cnt = 0;
    for(int l=1,r;l<=n;l=r+1){
        r = n / (n / l);
        id[++cnt] = r;
        m[n/l] = cnt;
    }
    for(int i=1;i<=cnt;i++) a[1][i] = id[i];
    for(int i=1;i<=cnt;i++) di[i] = m[n/(n/id[i])];
    for(int i=2;i<=k;i++){
        for(int j=1;j<=cnt;j++){
            a[i][j] = (a[i][j-1] + (id[j]-id[j-1]) * a[i-1][di[j]] % mod) % mod;
        }
    }
    cout<<a[k][cnt]<<endl;
}