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;
using ll = long long;
const ll MOD = 1000000007;
const ll M = 128;
const ll X = 32768; // >= sqrt(N)

ll a[M][X], b[M][X];
int main(){
	int N, K; scanf("%d%d", &N, &K);
	for(int i=1; i<X; i++){
		a[1][i] = min(i, N);
		b[1][i] = N/i;
	}
	for(int m=2; m<=K; m++){
		a[m][0]=0;
		for(int i=1; i<X; i++){
			a[m][i] = ( a[m][i-1] + b[m-1][i] ) % MOD;
		}
		b[m][X-1]= a[m][N/(X-1)];
		for(int i=X-2; i>=1; i--){
			b[m][i] = ( b[m][i+1] + a[m-1][i] * (N/i - N/(i+1)) ) % MOD;
		}
	}
	printf("%lld\n", b[K][1]);
}