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:

import sys

input = lambda: sys.stdin.readline().rstrip("\r\n")




MOD=10**9+7
n,k=map(int,input().split())

dd={}
for i in range(2,n+1):
    dd[i]=[]
    for a in range(i,n+1,i):
        dd[i].append(a)

dp=[[1]*(n+1) for i in range(k+1)]


for i in range(2,k+1):
    for a in range(2,n+1):
        h=dp[i-1][a]%MOD
        for c in dd[a]:
            dp[i][c]+=h
            dp[i][c]%=MOD
print((sum(dp[-1])-1)%(MOD))