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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;

#define ll long long
#define N 110
#define M 100010
#define pii pair <int, int>
#define fi first
#define se second
const ll p = 1e9 + 7;
int n, k;
ll f[N][M];
pii g[M]; 
map <int, int> mp;

int main() {
	while (scanf("%d%d", &k, &n) != EOF) {
		memset(f, 0, sizeof f);
		mp.clear();
		int m = 0;
		for (int i = 1, j; i <= k; i = j + 1) {
			j = k / (k / i);
			g[++m] = pii(j, j - i + 1);
			mp[j] = m;
		}
		for (int i = 1; i <= m; ++i) {
			f[1][i] = (f[1][i - 1] + g[i].se) % p; 
		}
		for (int i = 2; i <= n; ++i) {
			for (int j = 1; j <= m; ++j) {
				f[i][j] = (f[i][j - 1] + 1ll * g[j].se * f[i - 1][mp[k / g[j].fi]] % p) % p;
			}
		}
		printf("%lld\n", f[n][m]);
	}
	return 0;
}