#include "bits/stdc++.h"

using namespace std;
typedef long long ll;
ll MOD = 1e9 + 7;
ll dp[101][200001];
ll sdp[200001];
int num[200001];
int main() {
	int N, K;
	cin >> N >> K;
	int M = 0;
	int i = 1;
	while (i <= N) {
		int j = N / i;
		if (i <= j) {
			num[M++] = 1;
			i++;
		}
		else {
			num[M++] = N / j - i + 1;
			i = N / j + 1;
		}
	}
	dp[0][0] = 1;
	for (int k = 0; k < K; k++) {
		memset(sdp, 0, sizeof(sdp));
		sdp[0] = dp[k][0];
		for (int j = 1; j < M; j++) {
			sdp[j] = (sdp[j - 1] + dp[k][j]) % MOD;
		}
		for (int j = 0; j < M; j++) {
			dp[k + 1][j] = sdp[M - j - 1] * num[j] % MOD;
		}
	}
	ll ans = 0;
	for (int i = 0; i < M; i++) (ans += dp[K][i]) %= MOD;
	cout << ans << endl;
}
### Prompt

Please provide a cpp coded solution to the problem described below:

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;
typedef long long ll;
ll MOD = 1e9 + 7;
ll dp[101][200001];
ll sdp[200001];
int num[200001];
int main() {
	int N, K;
	cin >> N >> K;
	int M = 0;
	int i = 1;
	while (i <= N) {
		int j = N / i;
		if (i <= j) {
			num[M++] = 1;
			i++;
		}
		else {
			num[M++] = N / j - i + 1;
			i = N / j + 1;
		}
	}
	dp[0][0] = 1;
	for (int k = 0; k < K; k++) {
		memset(sdp, 0, sizeof(sdp));
		sdp[0] = dp[k][0];
		for (int j = 1; j < M; j++) {
			sdp[j] = (sdp[j - 1] + dp[k][j]) % MOD;
		}
		for (int j = 0; j < M; j++) {
			dp[k + 1][j] = sdp[M - j - 1] * num[j] % MOD;
		}
	}
	ll ans = 0;
	for (int i = 0; i < M; i++) (ans += dp[K][i]) %= MOD;
	cout << ans << endl;
}
```