Buggy python submission (verdict: Runtime Error):
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0

def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m

MOD = 10**9+7
x, y = map(int, input().split())
if (x+y)%3 != 0 or 3*x < x+y or 3*y < x+y:
    print(0)
    exit()
n = (x+y)//3
x -= n
y -= n
fact = [0, 1]
for i in range(2,n+1):
    fact.append(fact[i-1] * i % MOD)
factX = fact[x]
factY = fact[y]
factN = fact[n]

c = factN * modinv(factX, MOD) * modinv(factY, MOD)
c %= MOD
print(c)


Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0

def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m

MOD = 10**9+7
x, y = map(int, input().split())
if (x+y)%3 != 0 or 3*x < x+y or 3*y < x+y:
    print(0)
    exit()
n = (x+y)//3
x -= n
y -= n
fact = [1, 1]
for i in range(2,n+1):
    fact.append(fact[i-1] * i % MOD)
factX = fact[x]
factY = fact[y]
factN = fact[n]
# print(x,y,n)
# print(factX,factY,factN)

c = factN * modinv(factX, MOD) * modinv(factY, MOD)
c %= MOD
print(c)

Buggy python submission (verdict: Runtime Error):
MOD = 10**9+7
x, y = map(int, input().split())
if (x+y)%3 != 0 or 3*x < x+y or 3*y < x+y:
    print(0)
    exit()
n = (x+y)//3
x -= n
y -= n
fact = [0, 1]
for i in range(2,n+1):
    fact.append(fact[i-1] * i)
factX = fact[x]
factY = fact[y]
factN = fact[n]

inv_t = [0, 1]
for i in range(2,n+1):
    inv_t.append(inv_t[MOD % i] * (MOD - int(MOD / i)) % MOD)

c = factN * inv_t[factX] * inv_t[factY]
c %= MOD
print(c)



Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0

def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m

MOD = 10**9+7
x, y = map(int, input().split())
if (x+y)%3 != 0 or 3*x < x+y or 3*y < x+y:
    print(0)
    exit()
n = (x+y)//3
x -= n
y -= n
fact = [1, 1]
for i in range(2,n+1):
    fact.append(fact[i-1] * i % MOD)
factX = fact[x]
factY = fact[y]
factN = fact[n]
# print(x,y,n)
# print(factX,factY,factN)

c = factN * modinv(factX, MOD) * modinv(factY, MOD)
c %= MOD
print(c)

Buggy python submission (verdict: Time Limit Exceeded):
import math
MOD = 10**9+7
x, y = map(int, input().split())
if (x+y)%3 != 0 or 3*x < x+y or 3*y < x+y:
    print(0)
    exit()
n = (x+y)//3
x -= n
y -= n
factX = factY = factN = 1
for i in range(2,n+1):
    factN *= i % MOD
    if i == x: factX = factN
    if i == y: factY = factN

inv_t = [0]+[1]
for i in range(2,max(factX,factY)+1):
    inv_t += [inv_t[MOD % i] * (MOD - int(MOD / i)) % MOD]

# print(x,y,n)
# print(factN)
# print(inv_t[x],inv_t[y])

c = factN * inv_t[factX] * inv_t[factY]
c %= MOD
print(c)



Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0

def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m

MOD = 10**9+7
x, y = map(int, input().split())
if (x+y)%3 != 0 or 3*x < x+y or 3*y < x+y:
    print(0)
    exit()
n = (x+y)//3
x -= n
y -= n
fact = [1, 1]
for i in range(2,n+1):
    fact.append(fact[i-1] * i % MOD)
factX = fact[x]
factY = fact[y]
factN = fact[n]
# print(x,y,n)
# print(factX,factY,factN)

c = factN * modinv(factX, MOD) * modinv(factY, MOD)
c %= MOD
print(c)

Buggy python submission (verdict: Time Limit Exceeded):
import math
MOD = 10**9+7
x, y = map(int, input().split())
if (x+y)%3 != 0 or 3*x < x+y or 3*y < x+y:
    print(0)
    exit()
n = (x+y)//3
x -= n
y -= n
factX = factY = factN = 1
for i in range(1,n+1):
    factN *= i
    if i == x: factX = factN
    if i == y: factY = factN
c = factN // factX // factY
print(c%MOD)


Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0

def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m

MOD = 10**9+7
x, y = map(int, input().split())
if (x+y)%3 != 0 or 3*x < x+y or 3*y < x+y:
    print(0)
    exit()
n = (x+y)//3
x -= n
y -= n
fact = [1, 1]
for i in range(2,n+1):
    fact.append(fact[i-1] * i % MOD)
factX = fact[x]
factY = fact[y]
factN = fact[n]
# print(x,y,n)
# print(factX,factY,factN)

c = factN * modinv(factX, MOD) * modinv(factY, MOD)
c %= MOD
print(c)

Buggy python submission (verdict: Runtime Error):
import math
MOD = 10**9+7
x, y = map(int, input().split())
if (x+y)%3 != 0 or 3*x < x+y or 3*y < x+y:
    print(0)
    exit()
n = (x+y)//3
x -= n
y -= n
factN = 1
for i in range(1,n+1):
    factN *= i
    if i == x: factX = factN
    if i == y: factY = factN
c = factN // factX // factY
print(c%MOD)


Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0

def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m

MOD = 10**9+7
x, y = map(int, input().split())
if (x+y)%3 != 0 or 3*x < x+y or 3*y < x+y:
    print(0)
    exit()
n = (x+y)//3
x -= n
y -= n
fact = [1, 1]
for i in range(2,n+1):
    fact.append(fact[i-1] * i % MOD)
factX = fact[x]
factY = fact[y]
factN = fact[n]
# print(x,y,n)
# print(factX,factY,factN)

c = factN * modinv(factX, MOD) * modinv(factY, MOD)
c %= MOD
print(c)

Buggy python submission (verdict: Time Limit Exceeded):
import math
MOD = 10**9+7
x, y = map(int, input().split())
if (x+y)%3 != 0 or 3*x < x+y or 3*y < x+y:
    print(0)
    exit()
n = (x+y)//3
x -= n
y -= n
c = math.factorial(n) // math.factorial(x) // math.factorial(y)
print(c%MOD)


Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0

def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m

MOD = 10**9+7
x, y = map(int, input().split())
if (x+y)%3 != 0 or 3*x < x+y or 3*y < x+y:
    print(0)
    exit()
n = (x+y)//3
x -= n
y -= n
fact = [1, 1]
for i in range(2,n+1):
    fact.append(fact[i-1] * i % MOD)
factX = fact[x]
factY = fact[y]
factN = fact[n]
# print(x,y,n)
# print(factX,factY,factN)

c = factN * modinv(factX, MOD) * modinv(factY, MOD)
c %= MOD
print(c)

Buggy python submission (verdict: Runtime Error):
import math
MOD = 10**9+7
x, y = map(int, input().split())
if (x+y)%3 != 0 or 3*x < x+y or 3*y < x+y:
    print(0)
    exit()
n = (x+y)//3
x -= n
y -= n
c = math.factorial(x) // (math.factorial(x - y) * math.factorial(y))
print(c%MOD)


Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0

def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m

MOD = 10**9+7
x, y = map(int, input().split())
if (x+y)%3 != 0 or 3*x < x+y or 3*y < x+y:
    print(0)
    exit()
n = (x+y)//3
x -= n
y -= n
fact = [1, 1]
for i in range(2,n+1):
    fact.append(fact[i-1] * i % MOD)
factX = fact[x]
factY = fact[y]
factN = fact[n]
# print(x,y,n)
# print(factX,factY,factN)

c = factN * modinv(factX, MOD) * modinv(factY, MOD)
c %= MOD
print(c)

Buggy python submission (verdict: Runtime Error):
import math
MOD = 10**9+7
x, y = map(int, input().split())
if (x+y)%3 != 0 or 3*x < x+y or 3*y < x+y:
    print(0)
    exit()
n = (x+y)//3
x -= n
y -= n
c = math.factorial(x) // (math.factorial(x - y) * math.factorial(y))
print(c//MOD)


Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0

def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m

MOD = 10**9+7
x, y = map(int, input().split())
if (x+y)%3 != 0 or 3*x < x+y or 3*y < x+y:
    print(0)
    exit()
n = (x+y)//3
x -= n
y -= n
fact = [1, 1]
for i in range(2,n+1):
    fact.append(fact[i-1] * i % MOD)
factX = fact[x]
factY = fact[y]
factN = fact[n]
# print(x,y,n)
# print(factX,factY,factN)

c = factN * modinv(factX, MOD) * modinv(factY, MOD)
c %= MOD
print(c)

Buggy python submission (verdict: Runtime Error):
import math
MOD = 10**9+7
x, y = map(int, input().split())
if (x+y)%3 != 0 or 3*x < x+y or 3*y < x+y:
    print(0)
    exit()
n = (x+y)//3
x -= n
y -= n
c = math.factorial(n) // (math.factorial(n - r) * math.factorial(r))
print(c//MOD)


Fixed submission:
def xgcd(a, b):
    x0, y0, x1, y1 = 1, 0, 0, 1
    while b != 0:
        q, a, b = a // b, b, a % b
        x0, x1 = x1, x0 - q * x1
        y0, y1 = y1, y0 - q * y1
    return a, x0, y0

def modinv(a, m):
    g, x, y = xgcd(a, m)
    if g != 1:
        raise Exception('modular inverse does not exist')
    else:
        return x % m

MOD = 10**9+7
x, y = map(int, input().split())
if (x+y)%3 != 0 or 3*x < x+y or 3*y < x+y:
    print(0)
    exit()
n = (x+y)//3
x -= n
y -= n
fact = [1, 1]
for i in range(2,n+1):
    fact.append(fact[i-1] * i % MOD)
factX = fact[x]
factY = fact[y]
factN = fact[n]
# print(x,y,n)
# print(factX,factY,factN)

c = factN * modinv(factX, MOD) * modinv(factY, MOD)
c %= MOD
print(c)