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:
n, k = map(int, input().split())
dp, total = [[0 for i in range(n + 1)] for j in range(k + 1)], 0 # dp[len][max]

for i in range(n + 1): # when the max is 1 there is only 1 sequence
    dp[1][i] = 1
for i in range(2, k + 1): # higher maximum value
    for j in range(1, n + 1): # longer length
        for kk in range(j, n + 1, j): # follow the factors
            dp[i][kk] = (dp[i][kk] + dp[i - 1][j]) % 1000000007
for i in range(1, n + 1): # add all the sequences of length k
    total = (total + dp[k][i]) % 1000000007
print(total)