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 mashmokh
{
    static Integer[][] memo;
    
    public static void main (String[] args)
    {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt(), k = in.nextInt();
        memo = new Integer[n+1][k+1];
        
        int ans = 0;
        for (int i = 1; i <= n; i++)
        {
            ans += dp(i, k-1);
            ans %= 1000000007;
        }
            
        System.out.println(ans);
        
        in.close();
    }
    
    public static int dp(int n, int k)
    {
        if (k == 0)
            return 1;
        
        if (memo[n][k] != null)
            return memo[n][k];
            
        int ans = 0;
        for (int i = n; i <= memo.length-1; i += n)
        {
                ans += dp(i, k-1);
                ans %= 1000000007;
        }
            
        return memo[n][k] = ans;
    }
}