// Crt. 2019-10-24  14:34:54
#include <algorithm>
#include <iostream>
#include <cstdio>
using namespace std;
const int Mod = 1e9 + 7;

int n, m, f[102][100005], sum[100005];
int R[100005], val[100005];

int main() {
    cin >> m >> n;

    int cnt = 0;
    for (int l = 1, r; l <= m; l = r + 1)
        r = m / (m / l), R[++cnt] = r, val[cnt] = f[1][cnt] = r - l + 1;

    for (int i = 2; i <= n; ++i) {
        for (int j = 1; j <= cnt; ++j)
            sum[j] = (sum[j - 1] + f[i - 1][j]) % Mod;
        int pos = cnt;
        for (int j = 1; j <= cnt; ++j) {
            while (R[pos] > m / R[j]) --pos;
            f[i][j] = 1ll * val[j] * sum[pos] % Mod;
        }
    }

    int ans = 0;
    for (int i = 1; i <= cnt; ++i)
        ans = (ans + f[n][i]) % Mod;

    cout << ans << endl;

    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
// Crt. 2019-10-24  14:34:54
#include <algorithm>
#include <iostream>
#include <cstdio>
using namespace std;
const int Mod = 1e9 + 7;

int n, m, f[102][100005], sum[100005];
int R[100005], val[100005];

int main() {
    cin >> m >> n;

    int cnt = 0;
    for (int l = 1, r; l <= m; l = r + 1)
        r = m / (m / l), R[++cnt] = r, val[cnt] = f[1][cnt] = r - l + 1;

    for (int i = 2; i <= n; ++i) {
        for (int j = 1; j <= cnt; ++j)
            sum[j] = (sum[j - 1] + f[i - 1][j]) % Mod;
        int pos = cnt;
        for (int j = 1; j <= cnt; ++j) {
            while (R[pos] > m / R[j]) --pos;
            f[i][j] = 1ll * val[j] * sum[pos] % Mod;
        }
    }

    int ans = 0;
    for (int i = 1; i <= cnt; ++i)
        ans = (ans + f[n][i]) % Mod;

    cout << ans << endl;

    return 0;
}

```