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 ;
const int Mod = 1000000007 ;
const int MaxN = 100 + 10 ;
const int MaxM = 1000000 + 10 ;
int N , M , K , Dp[2][MaxM] , Len[MaxM] , Max[MaxM] , Bit ;
map<int,int> Map ;
int main() {
	scanf( "%d%d" , &M , &N ) ;
	for(register int L = 1 , R ; L <= M ; L = R + 1 ) {
		R = M / ( M / L ) ;
		Map[R] = ++K ;
		Len[K] = R - L + 1 ;
		Max[K] = R ;
	}
	for(register int i = 0 ; ++i <= K ; )
		Dp[0][i] = 1 ;
	while( N-- ) {
		Bit ^= 1 ;
		for(register int i = 0 ; ++i <= K ; ) {
			assert( Map[M/Max[i]] ) ;
			Dp[Bit][i] = ( Dp[Bit][i-1] + 1ll * Len[i] * Dp[Bit^1][Map[M/Max[i]]] % Mod ) % Mod ;
		}
	}
	return not printf( "%d\n" , Dp[Bit][K] ) ;
}