#include <bits/stdc++.h>

using namespace std;

const int MaxN = 1e5 + 15;
const int MaxK = 1e2 + 12;
const int MOD = 1e9 + 7;

int dp[MaxK][MaxN];
int n, k;
int d[MaxN], rd[MaxN];
map<int, int> pos;

int main() {
    cin >> n >> k;
    
    int cnt = 0;
    for(int l = 1; l <= n;)
    {
        ++cnt;
        d[cnt] = n / (n / l);
        pos[d[cnt]] = cnt;
        rd[cnt] = n / d[cnt];
        l = d[cnt] + 1;
    }
    
    for(int i = 1; i <= cnt; ++i)
        dp[1][i] = d[i];
        
    for(int i = 2; i <= k; ++i)
    {
        for(int j = 1; j <= cnt; ++j)
        {
            dp[i][j] = dp[i][j - 1] + (long long) (d[j] - d[j - 1]) * dp[i - 1][pos[rd[j]]] % MOD;
            dp[i][j] %= MOD;
        }
    }
    
    cout << dp[k][cnt] << '\n';
    
    return 0;
}
### Prompt

Generate 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 <bits/stdc++.h>

using namespace std;

const int MaxN = 1e5 + 15;
const int MaxK = 1e2 + 12;
const int MOD = 1e9 + 7;

int dp[MaxK][MaxN];
int n, k;
int d[MaxN], rd[MaxN];
map<int, int> pos;

int main() {
    cin >> n >> k;
    
    int cnt = 0;
    for(int l = 1; l <= n;)
    {
        ++cnt;
        d[cnt] = n / (n / l);
        pos[d[cnt]] = cnt;
        rd[cnt] = n / d[cnt];
        l = d[cnt] + 1;
    }
    
    for(int i = 1; i <= cnt; ++i)
        dp[1][i] = d[i];
        
    for(int i = 2; i <= k; ++i)
    {
        for(int j = 1; j <= cnt; ++j)
        {
            dp[i][j] = dp[i][j - 1] + (long long) (d[j] - d[j - 1]) * dp[i - 1][pos[rd[j]]] % MOD;
            dp[i][j] %= MOD;
        }
    }
    
    cout << dp[k][cnt] << '\n';
    
    return 0;
}
```