Problem: Mashmokh's boss, Bimokh, didn't like Mashmokh. So he fired him. Mashmokh decided to go to university and participate in ACM instead of finding a new job. He wants to become a member of Bamokh's team. In order to join he was given some programming tasks and one week to solve them. Mashmokh is not a very experienced programmer. Actually he is not a programmer at all. So he wasn't able to solve them. That's why he asked you to help him with these tasks. One of these tasks is the following.

A sequence of l integers b1, b2, ..., bl (1 ≤ b1 ≤ b2 ≤ ... ≤ bl ≤ n) is called good if each number divides (without a remainder) by the next number in the sequence. More formally <image> for all i (1 ≤ i ≤ l - 1).

Given n and k find the number of good sequences of length k. As the answer can be rather large print it modulo 1000000007 (109 + 7).

Input

The first line of input contains two space-separated integers n, k (1 ≤ n, k ≤ 2000).

Output

Output a single integer — the number of good sequences of length k modulo 1000000007 (109 + 7).

Examples

Input

3 2


Output

5


Input

6 4


Output

39


Input

2 1


Output

2

Note

In the first sample the good sequences are: [1, 1], [2, 2], [3, 3], [1, 2], [1, 3].

Solution (in JAVA):

Solution:
import java.util.*;

public class Test {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int k = sc.nextInt();
        long arr[][] = new long[n+1][k+1];
        ArrayList<ArrayList<Integer>> factor = new ArrayList<>();
        for(int i=0;i<=n;i++){
            ArrayList<Integer> temp = new ArrayList<>();
            factor.add(i,temp);
        }
        for(int i=1;i<=n;i++){
            ArrayList<Integer> temp = factor.get(i);
            for(int j =1;j<=i;j++){
                if(i%j==0)
                    temp.add(j);
            }
        }
        for(int i=0;i<=n;i++){
            for(int j=0;j<=k;j++)
                arr[i][j]=0;
        }
        for(int i=1;i<=n;i++){
            arr[i][1]=1;
        }
        for(int i =2;i<=k;i++){
            for(int j=1;j<=n;j++){
                ArrayList<Integer> temp = factor.get(j);
                for(int val : temp){
                    arr[j][i]= (arr[j][i]+arr[val][i-1])%1000000007;
                }
            }
        }
        long sum=0;
        for(int i=1;i<=n;i++){
           sum= sum + arr[i][k]; 
        }
        System.out.println(sum%1000000007);
}
}