Buggy python submission (verdict: Time Limit Exceeded):
import math
import os
import sys
from collections import defaultdict
from functools import lru_cache

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()))


@lru_cache(maxsize=None)
def next_max(n):
    # ある数と隣り合わせになれる数
    return int(N // n)


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


@lru_cache(maxsize=None)
def rec(n, k):
    if n <= 0:
        return 0
    if k <= 1:
        return n

    i = next_max(n)
    p = NM[i] if i < len(NM) else 1
    ret = rec(i, k - 1) * p % MOD
    cum = rec(n - p, k)
    return (cum + ret) % MOD


cnt = N
nums = []
while cnt >= 1:
    nums.append(cnt)
    i = next_max(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 = next_max(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)


Fixed submission:
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)

Buggy python submission (verdict: Time Limit Exceeded):
import math
import os
import sys
from functools import lru_cache

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()))


@lru_cache(maxsize=None)
def next_max(n):
    # ある数と隣り合わせになれる数
    return int(N // n)


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


# @lru_cache(maxsize=None)
# @debug
# def rec1(n, k):
#     if k <= 1:
#         return n
#
#     ret = 0
#     cnt = n
#     while cnt > 0:
#         i = next_max(cnt)
#         p = NM[i] if i < len(NM) else 1
#         ret = (ret + rec1(i, k - 1) * p) % MOD
#         cnt -= p
#     return ret
#
#
# #
# # ans = rec1(N, K)
# # print(ans % MOD)


@lru_cache(maxsize=None)
def rec(n, k):
    if n <= 0:
        return 0
    if k <= 1:
        return n

    i = next_max(n)
    p = NM[i] if i < len(NM) else 1
    ret = rec(i, k - 1)
    cum = rec(n - p, k)
    ret = ret * p % MOD
    return (cum + ret) % MOD


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


Fixed submission:
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)