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

def answer(n, k):
    dp = [[1 for j in range(n+1)] for i in range(k+1)]
    M = 10**9 + 7
    for i in range(1, k):
        for j in range(2, n+1):
            t = j
            while t <= n:
                dp[i+1][t] = (dp[i+1][t] + dp[i][j]) % M
                t += j
    #print('dp=', dp)
    return (sum(dp[k]) -1) % M #b/c row 0 is 1 and nonsense.

def main():
    n, k = map(int, sys.stdin.readline().split())
    print(answer(n, k))
    return
main()