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>
#define N 105
#define V 31627

using namespace std;

const int mod = 1e9 + 7;

int n, K;
int f[N][V], g[N][V];
int cnt[V];

int main() {
	scanf("%d %d", &K, &n); /* 把 n, k 的定义反了一下*/
	
	int p = sqrt(K);
	
	for(int i = 1; i < p; ++i)
		cnt[i] = K / i - K / (i + 1);
	cnt[p] = K / p - p;
	
	for(int i = 1; i <= p; ++i) {
		f[1][i] = 1;
		g[1][i] = cnt[i];
	}
	
	for(int i = 1; i <= n; ++i) {
		int sum = 0;
		for(int j = 1; j <= p; ++j) {
			sum = (sum + f[i][j]) % mod;
			g[i + 1][j] = 1LL * sum * cnt[j] % mod;
		}
		for(int j = p; j >= 1; --j) {
			sum = (sum + g[i][j]) % mod;
			f[i + 1][j] = sum;
		}
	}
	
	printf("%d\n", f[n + 1][1]);
	return 0;
}