#include <bits/stdc++.h>
using namespace std;
using ll=long long;
using Graph=vector<vector<int>>;
#define MOD 1000000007

int main(){
  int N,K;
  cin>>N>>K;
  vector<int> a;
  for(int i=1;i*i<=N;i++){
    a.push_back(i);
    if(i!=N/i){
      a.push_back(N/i);
    }
  }
  sort(a.begin(),a.end());
  int n=a.size();
  vector<int> cnt(n);
  cnt[0]=1;
  for(int i=1;i<n;i++){
    cnt[i]=a[i]-a[i-1];
  }
  vector<vector<ll>> dp(K,vector<ll>(n));
  for(int i=0;i<n;i++){
    dp[0][i]=(ll)cnt[i];
  }
  for(int j=1;j<K;j++){
    ll sum=0;
    for(int i=n-1;i>=0;i--){
      sum+=dp[j-1][(n-1)-i];
      sum%=MOD;
      dp[j][i]=sum*(ll)cnt[i]%MOD;
    }
  }

  ll ans=0;
  for(int i=0;i<n;i++){
    ans+=dp[K-1][i];
    ans%=MOD;
  }
  cout<<ans<<endl;

}

### Prompt

Construct a Cpp code solution to the problem outlined:

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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll=long long;
using Graph=vector<vector<int>>;
#define MOD 1000000007

int main(){
  int N,K;
  cin>>N>>K;
  vector<int> a;
  for(int i=1;i*i<=N;i++){
    a.push_back(i);
    if(i!=N/i){
      a.push_back(N/i);
    }
  }
  sort(a.begin(),a.end());
  int n=a.size();
  vector<int> cnt(n);
  cnt[0]=1;
  for(int i=1;i<n;i++){
    cnt[i]=a[i]-a[i-1];
  }
  vector<vector<ll>> dp(K,vector<ll>(n));
  for(int i=0;i<n;i++){
    dp[0][i]=(ll)cnt[i];
  }
  for(int j=1;j<K;j++){
    ll sum=0;
    for(int i=n-1;i>=0;i--){
      sum+=dp[j-1][(n-1)-i];
      sum%=MOD;
      dp[j][i]=sum*(ll)cnt[i]%MOD;
    }
  }

  ll ans=0;
  for(int i=0;i<n;i++){
    ans+=dp[K-1][i];
    ans%=MOD;
  }
  cout<<ans<<endl;

}

```