#include <iostream>
#include <cstdio>
#define mod 1000000007

int f[110][101000];
int l[101000], r[101000];

int main()
{
	int n, m; scanf("%d%d", &n, &m);
	int tot = 0;
	int R;
	for(int L = 1; L <= n; L = R + 1)
	{
		R = n / (n / L);
		l[++tot] = L; r[tot] = R; 
	}
	f[0][1] = 1;
	int Ans = 0;
	for(int i = 1; i <= m; i++)
	{
		int k = 0, sum = 0;
		for(int j = tot; j >= 1; j--)
		{
			if(k + 1 <= tot && l[k + 1] * l[j] <= n) k++, sum = (sum + f[i - 1][k]) % mod;
			f[i][j] = 1ll * (r[j] - l[j] + 1) * sum % mod;
			if(i == m) Ans = (Ans + f[m][j]) % mod;
		}
	}
	printf("%d\n", Ans);
}
### Prompt

Please formulate 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 <cstdio>
#define mod 1000000007

int f[110][101000];
int l[101000], r[101000];

int main()
{
	int n, m; scanf("%d%d", &n, &m);
	int tot = 0;
	int R;
	for(int L = 1; L <= n; L = R + 1)
	{
		R = n / (n / L);
		l[++tot] = L; r[tot] = R; 
	}
	f[0][1] = 1;
	int Ans = 0;
	for(int i = 1; i <= m; i++)
	{
		int k = 0, sum = 0;
		for(int j = tot; j >= 1; j--)
		{
			if(k + 1 <= tot && l[k + 1] * l[j] <= n) k++, sum = (sum + f[i - 1][k]) % mod;
			f[i][j] = 1ll * (r[j] - l[j] + 1) * sum % mod;
			if(i == m) Ans = (Ans + f[m][j]) % mod;
		}
	}
	printf("%d\n", Ans);
}
```