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 JAVA):

Solution:
import java.util.*;

public class Main{
	public static void main(String[]$){
		long mod=(long)1e9+7;
		Scanner sc=new Scanner(System.in);
		int n=sc.nextInt();
		int k=sc.nextInt();
		sc.close();
		ArrayList<Integer>len=new ArrayList<>();
		int l=1;
		while(l<=n){
			int r=n/(n/l);
			len.add(r-l+1);
			l=r+1;
		}
		int q=len.size();
		long[]dp=new long[k*(q+1)];
		for(int j=1;j <=q;j++){
			dp[j]=len.get(j-1)+dp[j-1];
		}
		for(int i=1;i<k;i++){
			for(int j=1;j<=q;j++){
				int x=i*(q+1)+j;
				dp[x]=(dp[x-1]+dp[x-2*j]*len.get(j-1))%mod;
			}
		}
		System.out.println(dp[k*(q+1)-1]);
	}
}