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;
static const int64_t mod=1000000007;
int main(){
  int64_t N,K;cin>>N>>K;
  vector<int64_t>A;
  int64_t n=pow(N,0.5);
  for(int i=0;i<n;i++)
    A.push_back(1);if(n<N/n)A.push_back(N/n-n);
  for(int64_t i=n;2<=i;i--){
  int64_t a=(N/(i-1))-(N/i);
    A.push_back(a);
  }int M=A.size();
  vector<vector<int64_t>>dp(M,vector<int64_t>(K));
  for(int i=0;i<M;i++)dp[i][0]=A[i];
  for(int j=1;j<K;j++){
  int64_t a=0;
    for(int i=0;i<M;i++){
    a=(a+dp[i][j-1])%mod;
      dp[M-1-i][j]=(a*A[M-1-i])%mod;
    }
        }int64_t ans=0;
  for(int i=0;i<M;i++)
    ans=(ans+dp[i][K-1])%mod;
  cout<<ans<<endl;
  return 0;
}