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 PYTHON3):

Solution:
from math import sqrt,gcd,ceil,floor,log,factorial
from itertools import permutations,combinations
from collections import Counter, defaultdict


n,k = map(int,input().split())
mod=10**9+7
if n==1:
    print(1)
    
else:
    #keys = [i for i in range(1,n+1)]
    
    d=defaultdict(list)
    
    for i in range(1,n//2+1):
        for j in range(i+1,n+1):
            if j%i==0:
                d[i].append(j)
                
    dp = [0]+[1 for i in range(n)]
    
    for i in range(k-1):
        for i in range(1,n//2+1):
            if i==1:
                dp[i]=(sum(dp)%mod)
                
            else:
                for mul in d[i]:
                    dp[i]=(dp[i]+(dp[mul]%mod))%mod
    
    #print(d)
    #print(dp)                
    print(sum(dp)%mod)