#include <bits/stdc++.h>
#define X first
#define Y second
using namespace std;

typedef long long ll;
typedef pair<int, int> pii;

const ll Q = (ll)(1e9) + 7;
const int MAXR = 63245;
const int MAXK = 101;

ll len[MAXR];
ll ans[MAXK][MAXR];

int main() {
	ios_base::sync_with_stdio(0);

	int N, K;
	cin >> N >> K;

	int R = floor(sqrt(N));

	for(int r = 1; r <= R; r++) {
		len[r] = 1;
		len[2*R+1-r] = N/r - (r < R ? N/(r+1) : R);
		ans[0][r] = 1;
		ans[0][R+r] = 1;
	}

	for(int k = 1; k <= K; k++) {
		for(int r = 1; r <= 2*R; r++) {
			ll add = ans[k-1][2*R+1-r] * len[r];
			ans[k][r] += (ans[k][r-1] + add) % Q;
		}
	}

	cout << ans[K][2*R] << '\n';
	return 0;
}
### Prompt

Your challenge is to write 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>
#define X first
#define Y second
using namespace std;

typedef long long ll;
typedef pair<int, int> pii;

const ll Q = (ll)(1e9) + 7;
const int MAXR = 63245;
const int MAXK = 101;

ll len[MAXR];
ll ans[MAXK][MAXR];

int main() {
	ios_base::sync_with_stdio(0);

	int N, K;
	cin >> N >> K;

	int R = floor(sqrt(N));

	for(int r = 1; r <= R; r++) {
		len[r] = 1;
		len[2*R+1-r] = N/r - (r < R ? N/(r+1) : R);
		ans[0][r] = 1;
		ans[0][R+r] = 1;
	}

	for(int k = 1; k <= K; k++) {
		for(int r = 1; r <= 2*R; r++) {
			ll add = ans[k-1][2*R+1-r] * len[r];
			ans[k][r] += (ans[k][r-1] + add) % Q;
		}
	}

	cout << ans[K][2*R] << '\n';
	return 0;
}
```