Buggy python submission (verdict: Runtime Error):
s = int(input())
MOD = 10 ** 9 + 7
ans = 0
fact = [0] * 10000
fact[0], fact[1] = 1, 1
for i in range(2, 10000):
    fact[i] = (fact[i-1] * i) % MOD

def f(n, r):
    return fact[n] * pow(fact[n-r], -1, MOD) * pow(fact[r], -1, MOD)

for i in range(1, s//3+1):
    if i == 1:
        ans += 1
    else:
        m = s - i * 3
        ans += f(m+i-1, m)
        ans %= MOD
print(ans%MOD)

Fixed submission:
s = int(input())
MOD = 10 ** 9 + 7
ans = 0
fact = [0] * 10000
fact[0], fact[1] = 1, 1
for i in range(2, 10000):
    fact[i] = (fact[i-1] * i) % MOD

def f(n, r):
    return fact[n] * pow(fact[n-r], -1, MOD) * pow(fact[r], -1, MOD)

for i in range(1, s//3+1):
    if i == 1:
        ans += 1
    else:
        m = s - i * 3
        ans += f(m+i-1, m)
        ans %= MOD
print(ans%MOD)

Buggy python submission (verdict: Runtime Error):
s = int(input())
MOD = 10 ** 9 + 7
ans = 0
fact = [0] * 4000
fact[0], fact[1] = 1, 1
for i in range(2, 4000):
    fact[i] = (fact[i-1] * i) % MOD

def f(n, r):
    return (fact[n+(r-1)] * pow(fact[n], -1, MOD) * pow(fact[r-1], -1, MOD))%MOD

for i in range(1, s//3+1):
    if i == 1:
        ans += 1
    else:
        m = s - i * 3
        ans += f(m, i)
        ans %= MOD
print(ans%MOD)

Fixed submission:
s = int(input())
MOD = 10 ** 9 + 7
ans = 0
fact = [0] * 10000
fact[0], fact[1] = 1, 1
for i in range(2, 10000):
    fact[i] = (fact[i-1] * i) % MOD

def f(n, r):
    return fact[n] * pow(fact[n-r], -1, MOD) * pow(fact[r], -1, MOD)

for i in range(1, s//3+1):
    if i == 1:
        ans += 1
    else:
        m = s - i * 3
        ans += f(m+i-1, m)
        ans %= MOD
print(ans%MOD)

Buggy python submission (verdict: Runtime Error):
s = int(input())
MOD = 10 ** 9 + 7
ans = 0
fact = [0] * 4000
fact[0], fact[1] = 1, 1
for i in range(2, 4000):
    fact[i] = (fact[i-1] * i) % MOD

def f(n, r):
    return (fact[n+(r-1)] * pow(fact[n], -1, MOD) * pow(fact[i-1], -1, MOD))%MOD

for i in range(1, s//3+1):
    if i == 1:
        ans += 1
    else:
        m = s - i * 3
        ans += f(m, i)
        ans %= MOD
print(ans%MOD)

Fixed submission:
s = int(input())
MOD = 10 ** 9 + 7
ans = 0
fact = [0] * 10000
fact[0], fact[1] = 1, 1
for i in range(2, 10000):
    fact[i] = (fact[i-1] * i) % MOD

def f(n, r):
    return fact[n] * pow(fact[n-r], -1, MOD) * pow(fact[r], -1, MOD)

for i in range(1, s//3+1):
    if i == 1:
        ans += 1
    else:
        m = s - i * 3
        ans += f(m+i-1, m)
        ans %= MOD
print(ans%MOD)

Buggy python submission (verdict: Runtime Error):
s = int(input())
MOD = 10 ** 9 + 7
ans = 0
fact = [0] * 2001
fact[0], fact[1] = 1, 1
for i in range(2, 2001):
    fact[i] = (fact[i-1] * i) % MOD

def f(n, r):
    return (fact[n+(r-1)] * pow(fact[n], -1, MOD) * pow(fact[i-1], -1, MOD))%MOD

for i in range(1, s//3+1):
    if i == 1:
        ans += 1
    else:
        m = s - i * 3
        ans += f(m, i)
        ans %= MOD
print(ans%MOD)

Fixed submission:
s = int(input())
MOD = 10 ** 9 + 7
ans = 0
fact = [0] * 10000
fact[0], fact[1] = 1, 1
for i in range(2, 10000):
    fact[i] = (fact[i-1] * i) % MOD

def f(n, r):
    return fact[n] * pow(fact[n-r], -1, MOD) * pow(fact[r], -1, MOD)

for i in range(1, s//3+1):
    if i == 1:
        ans += 1
    else:
        m = s - i * 3
        ans += f(m+i-1, m)
        ans %= MOD
print(ans%MOD)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**7)
s = int(input())
ans = 0
summ = 0
MOD = 10**9 + 7
def dfs(A):
    global ans, summ
    # print(A, summ)
    # summ = sum(A)
    if summ == s:
        ans += 1
        ans %= MOD
        return False
    elif summ < s:
        for i in range(3, s+1):
            if s - summ < 3:
                break
            A.append(i)
            summ += i
            if dfs(A) == False:
                summ -= A[-1]
                A.pop()
                break
            summ -= A[-1]
            A.pop()
        return True
    else:
        return False

dfs([])
print(ans%MOD)

Fixed submission:
s = int(input())
MOD = 10 ** 9 + 7
ans = 0
fact = [0] * 10000
fact[0], fact[1] = 1, 1
for i in range(2, 10000):
    fact[i] = (fact[i-1] * i) % MOD

def f(n, r):
    return fact[n] * pow(fact[n-r], -1, MOD) * pow(fact[r], -1, MOD)

for i in range(1, s//3+1):
    if i == 1:
        ans += 1
    else:
        m = s - i * 3
        ans += f(m+i-1, m)
        ans %= MOD
print(ans%MOD)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**7)
s = int(input())
ans = 0
MOD = 10**9 + 7
def dfs(A):
    # print(A)
    global ans
    summ = sum(A)
    if summ == s:
        ans += 1
        ans %= MOD
        return False
    elif summ < s:
        for i in range(3, s+1):
            if s - summ < 3:
                break
            A.append(i)
            if dfs(A) == False:
                A.pop()
                break
            A.pop()
        return True
    else:
        return False

dfs([])
print(ans%MOD)

Fixed submission:
s = int(input())
MOD = 10 ** 9 + 7
ans = 0
fact = [0] * 10000
fact[0], fact[1] = 1, 1
for i in range(2, 10000):
    fact[i] = (fact[i-1] * i) % MOD

def f(n, r):
    return fact[n] * pow(fact[n-r], -1, MOD) * pow(fact[r], -1, MOD)

for i in range(1, s//3+1):
    if i == 1:
        ans += 1
    else:
        m = s - i * 3
        ans += f(m+i-1, m)
        ans %= MOD
print(ans%MOD)