Problem: Find the number of sequences of length K consisting of positive integers such that the product of any two adjacent elements is at most N, modulo 10^9+7.

Constraints

* 1\leq N\leq 10^9
* ~~1~~ 2\leq K\leq 100 (fixed at 21:33 JST)
* N and K are integers.

Input

Input is given from Standard Input in the following format:


N K


Output

Print the number of sequences, modulo 10^9+7.

Examples

Input

3 2


Output

5


Input

10 3


Output

147


Input

314159265 35


Output

457397712

Solution (in PYTHON3):

Solution:
import math

n, k = map(int, input().split())
mod = 1000000007
n1 = int(math.sqrt(n))
if n1 * n1 == n:
    n2 = n1 - 1
else:
    n2 = n1

num = [n]
for i in range(1, n2):
    num.append(n // (i + 1))
    num[i - 1] -= num[i]
num[-1] -= n1

dp1 = [1      for i in range(n1)]
dp2 = [num[i] for i in range(n2)]
for _ in range(k - 1):
    l = sum(dp1) % mod
    newdp1 = [l for i in range(n1)]
    newdp2 = [0 for i in range(n2)]

    dp1sum = 0
    for j in range(0, n2):
        dp1sum = (dp1sum + dp1[j]) % mod
        newdp2[j] = (newdp2[j] + dp1sum * num[j]) % mod

    dp2sum = 0
    for j in range(n2 - 1, -1, -1):
        dp2sum = (dp2sum + dp2[j]) % mod
        newdp1[j] = (newdp1[j] + dp2sum) % mod
    dp1 = newdp1
    dp2 = newdp2
print((sum(dp1) + sum(dp2)) % mod)