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 math

def primeDec(n):
    res = []
    p = 2

    while p * p <= n:
        if n % p == 0:
            count = 0
            while n % p == 0:
                n //= p
                count += 1
            res.append((p, count))
        p += 1
    if n > 1:
        res.append((n, 1))

    return res

def comb(k, n):
    res = 1
    for i in range(n - k + 1, n + 1):
        res *= i
    for i in range(1, k + 1):
        res //= i
    return res

def ev(n, k):
    d = primeDec(n)
    res = 1

    for p, i in d:
        #print(k - 1, k + i - 1)
        res = (res * (comb(i, k + i - 1) % N)) % N
    #print(n, k, res)
    return res

N = 10 ** 9 + 7
n, k = map(int, input().split())
d = primeDec(n)
res = 0

for i in range(1, n + 1):
    res = (res + ev(i, k)) % N

print(res)