Buggy python submission (verdict: Runtime Error):
S = int(input())
mod = 10 ** 9 + 7
dp = [0 for _ in range(S)]
dp[0] = dp[1] = 0
dp[2] = dp[3] = 1

for i in range(3, S):
    dp[i] = (dp[i - 3] + dp[i - 1]) % mod
    
print(dp[-1])

Fixed submission:
import math


def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))

S = int(input())
ans = 0
mod = 10 ** 9 + 7
for i in range(1,700):
    x = S - 3 * i
    if x < 0:
        break
    ans += (combinations_count(x + i - 1, i - 1)) % mod
    ans %= mod
print(ans)

Buggy python submission (verdict: Runtime Error):
S = int(input())
mod = 10 ** 9 + 7
dp = [0 for _ in range(S)]
dp[0] = dp[1] = 0
dp[2] = dp[3] = 0

for i in range(S - 3):
    dp[i + 3] = (dp[i] + dp[i + 2]) % mod
    
print(dp[-1])

Fixed submission:
import math


def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))

S = int(input())
ans = 0
mod = 10 ** 9 + 7
for i in range(1,700):
    x = S - 3 * i
    if x < 0:
        break
    ans += (combinations_count(x + i - 1, i - 1)) % mod
    ans %= mod
print(ans)

Buggy python submission (verdict: Runtime Error):
from functools import lru_cache
@lru_cache(maxsize=None)
def dp(i):
    if i == 1 or i == 2:
        return 0
    elif i == 3 or i == 4:
        return 1
    else:
        return dp(i - 3) + dp(i - 1)


S = int(input())
print(dp(S))


Fixed submission:
import math


def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))

S = int(input())
ans = 0
mod = 10 ** 9 + 7
for i in range(1,700):
    x = S - 3 * i
    if x < 0:
        break
    ans += (combinations_count(x + i - 1, i - 1)) % mod
    ans %= mod
print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
def dp(i):
    if i == 1 or i == 2:
        return 0
    elif i == 3 or i == 4:
        return 1
    else:
        return dp(i - 3) + dp(i - 1)


S = int(input())
print(dp(S))


Fixed submission:
import math


def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))

S = int(input())
ans = 0
mod = 10 ** 9 + 7
for i in range(1,700):
    x = S - 3 * i
    if x < 0:
        break
    ans += (combinations_count(x + i - 1, i - 1)) % mod
    ans %= mod
print(ans)

Buggy python submission (verdict: Runtime Error):
def dp(i):
    if i == 1 or i == 2:
        return 0
    elif i == 3 or i == 4:
        return 1
    else:
        return dp[i - 3] + dp[i - 1]


S = int(input())
print(dp(S))


Fixed submission:
import math


def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))

S = int(input())
ans = 0
mod = 10 ** 9 + 7
for i in range(1,700):
    x = S - 3 * i
    if x < 0:
        break
    ans += (combinations_count(x + i - 1, i - 1)) % mod
    ans %= mod
print(ans)

Buggy python submission (verdict: Runtime Error):
import math
#n個からr個とるときの組み合わせの数
def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))

S = int(input())
ans = 0
mod = 10 ** 9 + 7
for i in range(1,S // 3 + 1):      #長さiの数列のとき
   
    x = S - 3 * i       #3を分配後の余り
    
    ans += (combinations_count(x + i - 1, i - 1)) % mod　#重複組み合わせを足す
    ans %= mod

print(ans)


Fixed submission:
import math


def combinations_count(n, r):
    return math.factorial(n) // (math.factorial(n - r) * math.factorial(r))

S = int(input())
ans = 0
mod = 10 ** 9 + 7
for i in range(1,700):
    x = S - 3 * i
    if x < 0:
        break
    ans += (combinations_count(x + i - 1, i - 1)) % mod
    ans %= mod
print(ans)