#include<iostream>
using namespace std;

const long long p = 1000000007;
long long dp[100000];
long long sum[100000];


int main() {
	long long n, k;
	long long m = 1;
	cin >> n >> k;
	while(m*m <= n) m++;
	m--;
	for(int i=0;i<n/(m+1);i++) dp[i] = 1;
	for(int i=0;i<m;i++) dp[n/(m+1)+i] = n/(m-i) - n/(m-i+1);
	sum[0] = dp[0];
	for(int i=1;i<m+n/(m+1);i++) sum[i] = dp[i] + sum[i-1];
	for(int l=1;l<k;l++) {
		for(int i=0;i<n/(m+1);i++) dp[i] = sum[n/(m+1)+m-i-1];
		for(int i=0;i<m;i++) dp[n/(m+1)+i] = (n/(m-i) - n/(m-i+1)) * sum[m-i-1] % p;
		sum[0] = dp[0];
		for(int i=1;i<m+n/(m+1);i++) sum[i] = (dp[i] + sum[i-1]) % p;
	}
	cout << sum[m+n/(m+1)-1] << endl;
	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<iostream>
using namespace std;

const long long p = 1000000007;
long long dp[100000];
long long sum[100000];


int main() {
	long long n, k;
	long long m = 1;
	cin >> n >> k;
	while(m*m <= n) m++;
	m--;
	for(int i=0;i<n/(m+1);i++) dp[i] = 1;
	for(int i=0;i<m;i++) dp[n/(m+1)+i] = n/(m-i) - n/(m-i+1);
	sum[0] = dp[0];
	for(int i=1;i<m+n/(m+1);i++) sum[i] = dp[i] + sum[i-1];
	for(int l=1;l<k;l++) {
		for(int i=0;i<n/(m+1);i++) dp[i] = sum[n/(m+1)+m-i-1];
		for(int i=0;i<m;i++) dp[n/(m+1)+i] = (n/(m-i) - n/(m-i+1)) * sum[m-i-1] % p;
		sum[0] = dp[0];
		for(int i=1;i<m+n/(m+1);i++) sum[i] = (dp[i] + sum[i-1]) % p;
	}
	cout << sum[m+n/(m+1)-1] << endl;
	return 0;
}

```