#include <iostream>
#include <vector>
#include <algorithm>
#include <cstring>
using namespace std;
typedef pair<int, int> pii;

int n, k, m;
long t;
vector<long> c, d;
long dp[110][100010];
const int MOD = 1e9 + 7;

int main(){
	cin >> n >> k;
	t = n;
	c.push_back(0);
	for (int i = 1; i*i <= n; ++i){
		c.push_back(i);
		c.push_back(n/i);
	}
	sort(c.begin(), c.end());
	for (auto i = 0; i < c.size()-1; ++i){
		d.push_back(c[i+1] - c[i]);
	}
	m = d.size();
	memset(dp, 0, sizeof(dp));
	dp[0][0] = 0;
	for (int j = 0; j < m; ++j) dp[0][j+1] = (dp[0][j] + d[j]) % MOD;
	for (int i = 1; i < k; ++i){
		for (int j = 1; j <= m; ++j){
			dp[i][j] = (dp[i][j-1] + (dp[i-1][m-j+1]*d[j-1])%MOD)%MOD;
		}
	}
	printf("%d", dp[k-1][m]);
}
### Prompt

Your task is to create a cpp solution 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 <iostream>
#include <vector>
#include <algorithm>
#include <cstring>
using namespace std;
typedef pair<int, int> pii;

int n, k, m;
long t;
vector<long> c, d;
long dp[110][100010];
const int MOD = 1e9 + 7;

int main(){
	cin >> n >> k;
	t = n;
	c.push_back(0);
	for (int i = 1; i*i <= n; ++i){
		c.push_back(i);
		c.push_back(n/i);
	}
	sort(c.begin(), c.end());
	for (auto i = 0; i < c.size()-1; ++i){
		d.push_back(c[i+1] - c[i]);
	}
	m = d.size();
	memset(dp, 0, sizeof(dp));
	dp[0][0] = 0;
	for (int j = 0; j < m; ++j) dp[0][j+1] = (dp[0][j] + d[j]) % MOD;
	for (int i = 1; i < k; ++i){
		for (int j = 1; j <= m; ++j){
			dp[i][j] = (dp[i][j-1] + (dp[i-1][m-j+1]*d[j-1])%MOD)%MOD;
		}
	}
	printf("%d", dp[k-1][m]);
}
```