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
from itertools import chain

N, K = map(int, input().split())

modulo = 10 ** 9 + 7
sqrtN  = int(math.sqrt(N))

P = [N // d for d in range(1, sqrtN + 1)]

# M[i] - 正の整数k個を並べたもののうち, 先頭がiで,
#        隣接する整数の積がN以下のものの個数 (mod modulo).

# k == 1 のときは M[i] == 1
M = {i: 1 for i in chain(P, range(1, P[-1]))}

# M2[i] - M[i] at k
# M2[i] = sum(M[j] for j such that 1 <= j <= N // i)
#       = M2[m] + sum(M[j] for j such that N//m < j <= N//i) (some m > i)
for k in range(2, K + 2):
    M2 = {}
    M2[N] = M[1]
    for m, i in zip(P, P[1:]):
        M2[i]  = M2[m] + sum(M[j] for j in range(N // m + 1, N // i + 1))
        M2[i] %= modulo
    for i in range(P[-1] - 1, 0, -1):
        M2[i]  = M2[i + 1] + M[N // i] * (N // i - N // (i + 1))
        M2[i] %= modulo
    M = M2

print(M[1])