Buggy python submission (verdict: Time Limit Exceeded):
mod = 10**9+7
N,K = map(int,input().split())
M = int(N**0.5)
dp = [[0]*M for _ in range(K+1)]
dp1 = [[0]*M for _ in range(K+1)]
dp2 = [[0]*M for _ in range(K+1)]

dp[0][0] = 1
dp1[0][0] = 1
dp2[0][0] = N
for m in range(1,M):
    dp[0][m] = 1
    dp1[0][m] = dp1[0][m-1]+dp[0][m]
    dp2[0][m] += dp2[0][m-1]+N//(m+1)*dp[0][m]

dp[1][0] = N
dp1[1][0] = N
dp2[1][0] = N**2
for m in range(1,M):
    dp[1][m] = N//(m+1)
    dp1[1][m] = dp1[1][m-1]+dp[1][m]
    dp2[1][m] += dp2[1][m-1]+N//(m+1)*dp[1][m]


for k in range(1,K):
    for m in range(M):
        dp[k+1][m] = dp1[k][M-1]+N//(m+1)*dp1[k-1][m]+dp2[k-1][M-1]-dp2[k-1][m]-M*dp1[k-1][M-1]
        dp[k+1][m] %= mod
        dp1[k+1][m] = dp1[k+1][m-1]+dp[k+1][m]
        dp1[k+1][m] %= mod
        dp2[k+1][m] = dp2[k+1][m-1]+N//(m+1)*dp[k+1][m]
        dp2[k+1][m] %= mod

print(dp[K][0])


Fixed submission:
from bisect import bisect
mod = 10**9+7
N,K = map(int,input().split())

c = []
for i in range(1,int(N**0.5)+1):
    c.append(i)
    c.append(int(N/i))
c = list(set(c))
c.sort()

k = []
for i in c:
    if int(N/i) != int(N/(i+1)):
        k.append(i)

dp = [[0]*len(k) for _ in range(K)]
for i in range(len(k)):
    dp[0][i]=k[i]

inv = [0]*(len(k)-1)
for i in range(len(k)-1):
    inv[i] = pow(k[i+1]-k[i],mod-2,mod)

index = [0]*len(k)
for i in range(len(k)):
    m = int(N/(k[i]+1))
    index[i] = bisect(k,m)

for i in range(K-1):
    dp[i+1][0] = dp[i][-1]
    for j in range(len(k)-1):
        m = int(N/(k[j]+1))
        l = index[j]
        S = dp[i][l-1]+(dp[i][l]-dp[i][l-1])*(m-k[l-1])*inv[l-1]
        dp[i+1][j+1] = dp[i+1][j]+(k[j+1]-k[j])*S
        dp[i+1][j+1] %= mod

print(dp[-1][-1])

Buggy python submission (verdict: Time Limit Exceeded):
from bisect import bisect
mod = 10**9+7
N,K = map(int,input().split())

c = []
for i in range(1,int(N**0.5)+1):
    c.append(i)
    c.append(int(N/i))
c = list(set(c))
c.sort()

k = []
for i in c:
    if int(N/i) != int(N/(i+1)):
        k.append(i)

dp = [[0]*len(k) for _ in range(K)]
for i in range(len(k)):
    dp[0][i]=k[i]

inv = [0]*(len(k)-1)
for i in range(len(k)-1):
    inv[i] = pow(k[i+1]-k[i],mod-2,mod)

index = [0]*len(k)
for i in range(len(k)):
    m = int(N/(k[i]+1))
    index[i] = bisect(k,m)

for i in range(K-1):
    dp[i+1][0] = dp[i][-1]
    for j in range(len(k)-1):
        m = int(N/(k[j]+1))
        l = index[j]
        S = dp[i][l-1]+(dp[i][l]-dp[i][l-1])*(m-k[l-1])*inv[l-1]
        dp[i+1][j+1] = dp[i+1][j]+(k[j+1]-k[j])*S
        dp[i+1][j+1] %= mod

print(dp[-1][-1])

Fixed submission:
from bisect import bisect
mod = 10**9+7
N,K = map(int,input().split())

c = []
for i in range(1,int(N**0.5)+1):
    c.append(i)
    c.append(int(N/i))
c = list(set(c))
c.sort()

k = []
for i in c:
    if int(N/i) != int(N/(i+1)):
        k.append(i)

dp = [[0]*len(k) for _ in range(K)]
for i in range(len(k)):
    dp[0][i]=k[i]

inv = [0]*(len(k)-1)
for i in range(len(k)-1):
    inv[i] = pow(k[i+1]-k[i],mod-2,mod)

index = [0]*len(k)
for i in range(len(k)):
    m = int(N/(k[i]+1))
    index[i] = bisect(k,m)

for i in range(K-1):
    dp[i+1][0] = dp[i][-1]
    for j in range(len(k)-1):
        m = int(N/(k[j]+1))
        l = index[j]
        S = dp[i][l-1]+(dp[i][l]-dp[i][l-1])*(m-k[l-1])*inv[l-1]
        dp[i+1][j+1] = dp[i+1][j]+(k[j+1]-k[j])*S
        dp[i+1][j+1] %= mod

print(dp[-1][-1])

Buggy python submission (verdict: Time Limit Exceeded):
from bisect import bisect
mod = 10**9+7
N,K = map(int,input().split())

c = []
for i in range(1,int(N**0.5)+1):
    c.append(i)
    c.append(int(N/i))
c = list(set(c))
c.sort()

k = []
for i in c:
    if int(N/i) != int(N/(i+1)):
        k.append(i)

dp = [[0]*len(k) for _ in range(K)]
for i in range(len(k)):
    dp[0][i]=k[i]

def S(n,m):
    l = bisect(k,m)
    return dp[n][l-1]+(dp[n][l]-dp[n][l-1])*(m-k[l-1])*pow(k[l]-k[l-1],mod-2,mod)

    
for i in range(K-1):
    dp[i+1][0] = dp[i][-1]
    for j in range(len(k)-1):
        dp[i+1][j+1] = dp[i+1][j]+(k[j+1]-k[j])*S(i,int(N/(k[j]+1)))
        dp[i+1][j+1] %= mod

print(dp[-1][-1])

Fixed submission:
from bisect import bisect
mod = 10**9+7
N,K = map(int,input().split())

c = []
for i in range(1,int(N**0.5)+1):
    c.append(i)
    c.append(int(N/i))
c = list(set(c))
c.sort()

k = []
for i in c:
    if int(N/i) != int(N/(i+1)):
        k.append(i)

dp = [[0]*len(k) for _ in range(K)]
for i in range(len(k)):
    dp[0][i]=k[i]

inv = [0]*(len(k)-1)
for i in range(len(k)-1):
    inv[i] = pow(k[i+1]-k[i],mod-2,mod)

index = [0]*len(k)
for i in range(len(k)):
    m = int(N/(k[i]+1))
    index[i] = bisect(k,m)

for i in range(K-1):
    dp[i+1][0] = dp[i][-1]
    for j in range(len(k)-1):
        m = int(N/(k[j]+1))
        l = index[j]
        S = dp[i][l-1]+(dp[i][l]-dp[i][l-1])*(m-k[l-1])*inv[l-1]
        dp[i+1][j+1] = dp[i+1][j]+(k[j+1]-k[j])*S
        dp[i+1][j+1] %= mod

print(dp[-1][-1])