Buggy python submission (verdict: Runtime Error):
inf = 10**9+7
import sys
a = 0
def nCr(n, r):
    r = min(r, n - r)
    if r == 0: return 1;
    if r == 1: return n;
    numerator = [n - r + i + 1 for i in range(r)]
    denominator  = [i + 1 for i in range(r)]
    for p in range(2, r + 1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p
            for k in range(p - 1, r, p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot
    result = 1
    for k in range(r):
        if numerator[k] > 1: 
            result = (result * numerator[k])%inf
    return result

x, y = map(int, input().split())
key = 0
if x == 2*y:
    print(1)
    sys.exit()
if y == 2*x:
    print(1)
    sys.exit()
while x>0 and y>0:
    x, y = x-3, y-3
    key += 1
    print(x/y)
    if x == 2*y:
        a = 1
        break
    if y == 2*x:
        a = -1
        break

if x < 0 or y < 0:
    print(0)
    sys.exit()
if a == 0:
    print(0)
    sys.exit()
if a == 1:
    print(int(nCr(key*2+y ,key)))
else:
    print(int(nCr(key*2+x ,key)))

Fixed submission:
inf = 10**9+7
import sys
a = 0
def nCr(n, r):
    r = min(r, n - r)
    if r == 0: return 1;
    if r == 1: return n;
    numerator = [n - r + i + 1 for i in range(r)]
    denominator  = [i + 1 for i in range(r)]
    for p in range(2, r + 1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p
            for k in range(p - 1, r, p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot
    result = 1
    for k in range(r):
        if numerator[k] > 1: 
            result = (result * numerator[k])%inf
    return result

x, y = map(int, input().split())
key = 0
if x == 2*y:
    print(1)
    sys.exit()
if y == 2*x:
    print(1)
    sys.exit()
while x>0 and y>0:
    x, y = x-3, y-3
    key += 1
    if x == 2*y:
        a = 1
        break
    if y == 2*x:
        a = -1
        break

if x < 0 or y < 0:
    print(0)
    sys.exit()

if a == 0:
    print(0)
elif a == 1:
    print(int(nCr(key*2+y ,key)))
else:
    print(int(nCr(key*2+x ,key)))

Buggy python submission (verdict: Runtime Error):
inf = 10**9+7
import sys

def nCr(n, r):
    r = min(r, n - r)
    if r == 0: return 1;
    if r == 1: return n;
    numerator = [n - r + i + 1 for i in range(r)]
    denominator  = [i + 1 for i in range(r)]
    for p in range(2, r + 1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p
            for k in range(p - 1, r, p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot
    result = 1
    for k in range(r):
        if numerator[k] > 1: 
            result = (result * numerator[k])%inf
    return result

x, y = map(int, input().split())
key = 0
if x == 2*y:
    print(1)
    sys.exit()
if y == 2*x:
    print(1)
    sys.exit()
while x>0 and y>0:
    x, y = x-3, y-3
    key += 1
    print(x/y)
    if x == 2*y:
        a = 1
        break
    if y == 2*x:
        a = -1
        break

if x < 0 or y < 0:
    print(0)
    sys.exit()
if not a:
    print(0)
if a == 1:
    print(int(nCr(key*2+y ,key)))
else:
    print(int(nCr(key*2+x ,key)))

Fixed submission:
inf = 10**9+7
import sys
a = 0
def nCr(n, r):
    r = min(r, n - r)
    if r == 0: return 1;
    if r == 1: return n;
    numerator = [n - r + i + 1 for i in range(r)]
    denominator  = [i + 1 for i in range(r)]
    for p in range(2, r + 1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p
            for k in range(p - 1, r, p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot
    result = 1
    for k in range(r):
        if numerator[k] > 1: 
            result = (result * numerator[k])%inf
    return result

x, y = map(int, input().split())
key = 0
if x == 2*y:
    print(1)
    sys.exit()
if y == 2*x:
    print(1)
    sys.exit()
while x>0 and y>0:
    x, y = x-3, y-3
    key += 1
    if x == 2*y:
        a = 1
        break
    if y == 2*x:
        a = -1
        break

if x < 0 or y < 0:
    print(0)
    sys.exit()

if a == 0:
    print(0)
elif a == 1:
    print(int(nCr(key*2+y ,key)))
else:
    print(int(nCr(key*2+x ,key)))

Buggy python submission (verdict: Runtime Error):
inf = 10**9+7

import sys

def nCr(n, r):
    r = min(r, n - r)
    if r == 0: return 1;
    if r == 1: return n;
    numerator = [n - r + i + 1 for i in range(r)]
    denominator  = [i + 1 for i in range(r)]
    for p in range(2, r + 1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p
            for k in range(p - 1, r, p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot
    result = 1
    for k in range(r):
        if numerator[k] > 1: 
            result = (result * numerator[k])%inf
    return result

x, y = map(int, input().split())
key = 0
if x == 2*y:
    print(1)
    sys.exit()
if y == 2*x:
    print(1)
    sys.exit()
while x>0 and y>0:
    x, y = x-3, y-3
    key += 1
    if x == 2*y:
        a = 1
        break
    if y == 2*x:
        a = -1
        break

if x < 0 or y < 0:
    print(0)
    sys.exit()

if a == 1:
    print(int(nCr(key*2+y ,key)))
else:
    print(int(nCr(key*2+x ,key)))
    

Fixed submission:
inf = 10**9+7
import sys
a = 0
def nCr(n, r):
    r = min(r, n - r)
    if r == 0: return 1;
    if r == 1: return n;
    numerator = [n - r + i + 1 for i in range(r)]
    denominator  = [i + 1 for i in range(r)]
    for p in range(2, r + 1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p
            for k in range(p - 1, r, p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot
    result = 1
    for k in range(r):
        if numerator[k] > 1: 
            result = (result * numerator[k])%inf
    return result

x, y = map(int, input().split())
key = 0
if x == 2*y:
    print(1)
    sys.exit()
if y == 2*x:
    print(1)
    sys.exit()
while x>0 and y>0:
    x, y = x-3, y-3
    key += 1
    if x == 2*y:
        a = 1
        break
    if y == 2*x:
        a = -1
        break

if x < 0 or y < 0:
    print(0)
    sys.exit()

if a == 0:
    print(0)
elif a == 1:
    print(int(nCr(key*2+y ,key)))
else:
    print(int(nCr(key*2+x ,key)))

Buggy python submission (verdict: Runtime Error):
inf = 10**9+7

import sys

def nCr(n, r):
    r = min(r, n - r)
    if r == 0: return 1;
    if r == 1: return n;
    numerator = [n - r + i + 1 for i in range(r)]
    denominator  = [i + 1 for i in range(r)]
    for p in range(2, r + 1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p
            for k in range(p - 1, r, p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot
    result = 1
    for k in range(r):
        if numerator[k] > 1: 
            result = (result * numerator[k])%inf
    return result

x, y = map(int, input().split())
key = 0
while x>0 and y>0:
    x, y = x-3, y-3
    key += 1
    if x == 2*y:
        a = 1
        break
    if y == 2*x:
        a = -1
        break

if x < 0 or y < 0:
    print(0)
    sys.exit()

if a == 1:
    print(int(nCr(key*2+y ,key)))
else:
    print(int(nCr(key*2+x ,key)))
    

Fixed submission:
inf = 10**9+7
import sys
a = 0
def nCr(n, r):
    r = min(r, n - r)
    if r == 0: return 1;
    if r == 1: return n;
    numerator = [n - r + i + 1 for i in range(r)]
    denominator  = [i + 1 for i in range(r)]
    for p in range(2, r + 1):
        pivot = denominator[p - 1]
        if pivot > 1:
            offset = (n - r) % p
            for k in range(p - 1, r, p):
                numerator[k - offset] /= pivot
                denominator[k] /= pivot
    result = 1
    for k in range(r):
        if numerator[k] > 1: 
            result = (result * numerator[k])%inf
    return result

x, y = map(int, input().split())
key = 0
if x == 2*y:
    print(1)
    sys.exit()
if y == 2*x:
    print(1)
    sys.exit()
while x>0 and y>0:
    x, y = x-3, y-3
    key += 1
    if x == 2*y:
        a = 1
        break
    if y == 2*x:
        a = -1
        break

if x < 0 or y < 0:
    print(0)
    sys.exit()

if a == 0:
    print(0)
elif a == 1:
    print(int(nCr(key*2+y ,key)))
else:
    print(int(nCr(key*2+x ,key)))