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
import os
import sys
from collections import defaultdict

if os.getenv("LOCAL"):
    sys.stdin = open("_in.txt", "r")

sys.setrecursionlimit(2147483647)
INF = float("inf")
IINF = 10 ** 18

MOD = 10 ** 9 + 7
N, K = list(map(int, sys.stdin.readline().split()))

NM = []
prev = 0
for i in range(1, int(math.sqrt(N)) + 2):
    m = int(N // i)
    NM.append(N - m - prev)
    prev = N - m

cnt = N
nums = []
while cnt >= 1:
    nums.append(cnt)
    i = int(N // cnt)
    p = NM[i] if i < len(NM) else 1
    cnt -= p
nums.reverse()

# dp[k][n]: rec(n, k)
dp = defaultdict(lambda: defaultdict(int))
for n in nums:
    dp[1][n] = n
for k in range(2, K + 1):
    for n in nums:
        i = int(N // n)
        p = NM[i] if i < len(NM) else 1
        ret = dp[k - 1][i] * p % MOD
        cum = dp[k][n - p]
        dp[k][n] = (cum + ret) % MOD

ans = dp[K][N]
print(ans % MOD)

# ans = rec(N, K)
# print(ans % MOD)