Buggy python submission (verdict: Runtime Error):
x,y = map(int,input().split())
mod = 10**9 + 7
if (x+y)%3 != 0:
    print(0)
    exit()
n = (x+y)//3
a = (2 * x - y) // 3
b = (2 * y - x) // 3
if a == 0 or b == 0:
    print(1)
    exit()
if a < 0 or b < 0:
    print(0)
    exit()
MAX = 10
fac = [1,1] + [0] * MAX
finv = [1,1] + [0] * MAX
inv = [0,1] + [0] * MAX
for i in range(2,MAX):
    fac[i] = fac[i-1] * i % mod
    inv[i] = -inv[mod%i] * (mod // i) % mod
    finv[i] = finv[i-1] * inv[i]%mod


def nCr(n,r):
    if n<r:
        return 0
    if n<0 or r<0:
        return 0
    return fac[n] * (finv[r] * finv[n-1]%mod)%mod

print(nCr(n,a))

Fixed submission:
x,y = map(int,input().split())
mod = 10**9 + 7
if (x+y)%3 != 0:
    print(0)
    exit()
n = (x+y)//3
a = (2 * x - y) // 3
b = (2 * y - x) // 3
if a == 0 or b == 0:
    print(1)
    exit()
if a < 0 or b < 0:
    print(0)
    exit()
MAX = 700000
fac = [1,1] + [0] * MAX     #累積積
finv = [1,1] + [0] * MAX    #modにおける逆元
inv = [0,1] + [0] * MAX     #invの累積積
for i in range(2,MAX):
    fac[i] = fac[i-1] * i % mod
    inv[i] = -inv[mod%i] * (mod//i)%mod
    finv[i] = finv[i-1] * inv[i]%mod


def nCr(n,r):
    if n<r:
        return 0
    if n<0 or r<0:
        return 0
    return fac[n] * (finv[r] * finv[n-r]%mod)%mod

print(nCr(n,a))

Buggy python submission (verdict: Runtime Error):
x,y = map(int,input().split())
mod = 10**9 + 7
if (x+y)%3 != 0:
    print(0)
    exit()
n = (x+y)//3
a = (2 * x - y) // 3
b = (2 * y - x) // 3
if a == 0 or b == 0:
    print(1)
    exit()
if a < 0 or b < 0:
    print(0)
    exit()
MAX = 10
fac = [1,1] + [0] * MAX     #累積積
finv = [1,1] + [0] * MAX    #modにおける逆元
inv = [0,1] + [0] * MAX     #invの累積積
for i in range(2,MAX):
    fac[i] = fac[i-1] * i % mod
    inv[i] = -inv[mod%i] * (mod//i)%mod
    finv[i] = finv[i-1] * inv[i]%mod


def nCr(n,r):
    if n<r:
        return 0
    if n<0 or r<0:
        return 0
    return fac[n] * (finv[r] * finv[n-1]%mod)%mod

print(nCr(n,a))

Fixed submission:
x,y = map(int,input().split())
mod = 10**9 + 7
if (x+y)%3 != 0:
    print(0)
    exit()
n = (x+y)//3
a = (2 * x - y) // 3
b = (2 * y - x) // 3
if a == 0 or b == 0:
    print(1)
    exit()
if a < 0 or b < 0:
    print(0)
    exit()
MAX = 700000
fac = [1,1] + [0] * MAX     #累積積
finv = [1,1] + [0] * MAX    #modにおける逆元
inv = [0,1] + [0] * MAX     #invの累積積
for i in range(2,MAX):
    fac[i] = fac[i-1] * i % mod
    inv[i] = -inv[mod%i] * (mod//i)%mod
    finv[i] = finv[i-1] * inv[i]%mod


def nCr(n,r):
    if n<r:
        return 0
    if n<0 or r<0:
        return 0
    return fac[n] * (finv[r] * finv[n-r]%mod)%mod

print(nCr(n,a))

Buggy python submission (verdict: Time Limit Exceeded):
from math import factorial
mod = 10**9+7
def comb(n,k,p):
    if n<0 or k<0 or n<k:
        return 0
    if n==0 or k==0:
        return 1
    a = factorial(n)%p
    b = factorial(k)%p
    c = factorial(n-k)%p
    return (a*power_func(b,p-2,p)*power_func(c,p-2,p))%p

def power_func(a,b,p):
    if b==0:
        return 1
    if b%2==0:
        d = power_func(a,b//2,p)
        return d*d %p
    if b%2 == 1:
        return (a*power_func(a,b-1,p ))%p

x,y = map(int,input().split())
if (x+y)%3 != 0:
    print(0)
else:
    n = (2*x - y)//3
    m = (2*y - x)//3
    if min(n,m) < 0:
        print(0)
        exit()
    ans = comb(n+m , n , mod)
    print(ans)

Fixed submission:
x,y = map(int,input().split())
mod = 10**9 + 7
if (x+y)%3 != 0:
    print(0)
    exit()
n = (x+y)//3
a = (2 * x - y) // 3
b = (2 * y - x) // 3
if a == 0 or b == 0:
    print(1)
    exit()
if a < 0 or b < 0:
    print(0)
    exit()
MAX = 700000
fac = [1,1] + [0] * MAX     #累積積
finv = [1,1] + [0] * MAX    #modにおける逆元
inv = [0,1] + [0] * MAX     #invの累積積
for i in range(2,MAX):
    fac[i] = fac[i-1] * i % mod
    inv[i] = -inv[mod%i] * (mod//i)%mod
    finv[i] = finv[i-1] * inv[i]%mod


def nCr(n,r):
    if n<r:
        return 0
    if n<0 or r<0:
        return 0
    return fac[n] * (finv[r] * finv[n-r]%mod)%mod

print(nCr(n,a))

Buggy python submission (verdict: Time Limit Exceeded):
from math import factorial
mod = 10**9+7
def comb(n,k,p):
    if n<0 or k<0 or n<k:
        return 0
    if n==0 or k==0:
        return 1
    a = factorial(n)%p
    b = factorial(k)%p
    c = factorial(n-k)%p
    return (a*power_func(b,p-2,p)*power_func(c,p-2,p))%p

def power_func(a,b,p):
    if b==0:
        return 1
    if b%2==0:
        d = power_func(a,b//2,p)
        return d*d %p
    if b%2 == 1:
        return (a*power_func(a,b-1,p ))%p

x,y = map(int,input().split())
if (x+y)%3 != 0:
    print(0)
else:
    n = (2*x - y)//3
    m = (2*y - x)//3
    if min(n,m) < 0:
        print(0)
        exit()
    ans = comb(n+m , n , mod)
    print(ans)

Fixed submission:
x,y = map(int,input().split())
mod = 10**9 + 7
if (x+y)%3 != 0:
    print(0)
    exit()
n = (x+y)//3
a = (2 * x - y) // 3
b = (2 * y - x) // 3
if a == 0 or b == 0:
    print(1)
    exit()
if a < 0 or b < 0:
    print(0)
    exit()
MAX = 700000
fac = [1,1] + [0] * MAX     #累積積
finv = [1,1] + [0] * MAX    #modにおける逆元
inv = [0,1] + [0] * MAX     #invの累積積
for i in range(2,MAX):
    fac[i] = fac[i-1] * i % mod
    inv[i] = -inv[mod%i] * (mod//i)%mod
    finv[i] = finv[i-1] * inv[i]%mod


def nCr(n,r):
    if n<r:
        return 0
    if n<0 or r<0:
        return 0
    return fac[n] * (finv[r] * finv[n-r]%mod)%mod

print(nCr(n,a))

Buggy python submission (verdict: Runtime Error):
mod = 10**9 + 7
x,y = map(int,input().split())
dp = [[0]*(y+3) for _ in range(x+3)]
dp[0][0] = 1

for i in range(x+1):
    for j in range(y+1):
        if dp[i][j] >= mod:
            dp[i][j] %= mod
        if dp[i][j] == 0:
            continue
        else:
            if i+2 <= x+1 and j+1 <= y+1:
                dp[i+2][j+1] += dp[i][j]
            if i+1 <= x+1 and j+2 <= y+1:
                dp[i+1][j+2] += dp[i][j]
print(dp[x][y])

Fixed submission:
x,y = map(int,input().split())
mod = 10**9 + 7
if (x+y)%3 != 0:
    print(0)
    exit()
n = (x+y)//3
a = (2 * x - y) // 3
b = (2 * y - x) // 3
if a == 0 or b == 0:
    print(1)
    exit()
if a < 0 or b < 0:
    print(0)
    exit()
MAX = 700000
fac = [1,1] + [0] * MAX     #累積積
finv = [1,1] + [0] * MAX    #modにおける逆元
inv = [0,1] + [0] * MAX     #invの累積積
for i in range(2,MAX):
    fac[i] = fac[i-1] * i % mod
    inv[i] = -inv[mod%i] * (mod//i)%mod
    finv[i] = finv[i-1] * inv[i]%mod


def nCr(n,r):
    if n<r:
        return 0
    if n<0 or r<0:
        return 0
    return fac[n] * (finv[r] * finv[n-r]%mod)%mod

print(nCr(n,a))