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())
d = 1000000007

n += 1
r = [{} for i in range(n)]  # multiples
for i in range(2, n):
    if r[i] == {}:
        for j in range(i, n, i): r[j][i] = 1
        q = i * i
        while q < n:
            for j in range(q, n, q): r[j][i] += 1
            q *= i

c = [1, k] + [0] * 9  # binomial
k -= 1
for i in range(2, 11): c[i] = (c[i - 1] * (k + i)) // i

s = -1
for q in r:
    p = 1
    for i in q.values(): p = p * c[i]
    s += p

print(s % d)