#include <bits/stdc++.h>
using namespace std;
#define int long long
#define REP(i,n) for(int i = 0;i < (int)(n);i++)
constexpr long long MOD = 1000000007;

signed main(){
	int N,K;
	cin>>N>>K;
	vector<int>p;
	for(int i=1;i*i<=N;i++){
		p.push_back(i);
		if(i != N/i)p.push_back(N/i);
	}
	sort(p.begin(),p.end());
	vector<int>mul;mul.push_back(1);
	REP(i,p.size()-1)mul.push_back(p[i+1]-p[i]);

	vector<int>dp(mul.size(),1);
	REP(i,K-1){
		vector<int>ndp(mul.size());
		int sum = 0;
		REP(j,mul.size()){
			(ndp[mul.size()-j-1] += dp[j] * mul[j] + sum) %= MOD;
			(sum += dp[j] * mul[j]) %= MOD;
		}
		dp = ndp;
	}
	int ans = 0;
	REP(i,mul.size())(ans += dp[i]*mul[i]) %= MOD;
	cout << ans << endl;
}
### Prompt

Please create a solution in CPP to the following 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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define REP(i,n) for(int i = 0;i < (int)(n);i++)
constexpr long long MOD = 1000000007;

signed main(){
	int N,K;
	cin>>N>>K;
	vector<int>p;
	for(int i=1;i*i<=N;i++){
		p.push_back(i);
		if(i != N/i)p.push_back(N/i);
	}
	sort(p.begin(),p.end());
	vector<int>mul;mul.push_back(1);
	REP(i,p.size()-1)mul.push_back(p[i+1]-p[i]);

	vector<int>dp(mul.size(),1);
	REP(i,K-1){
		vector<int>ndp(mul.size());
		int sum = 0;
		REP(j,mul.size()){
			(ndp[mul.size()-j-1] += dp[j] * mul[j] + sum) %= MOD;
			(sum += dp[j] * mul[j]) %= MOD;
		}
		dp = ndp;
	}
	int ans = 0;
	REP(i,mul.size())(ans += dp[i]*mul[i]) %= MOD;
	cout << ans << endl;
}
```