Buggy python submission (verdict: Runtime Error):
MOD = 10**9 + 7
X, Y = map(int, input().split())
  
if (X+Y)%3!=0:
  print(0)
  quit()
  
if X < Y:
  X, Y = Y, X

sub = X - Y
tan = Y - sub

X = sub + tan//3 + 3
Y = tan//3 + 3
dp = [[0]*X for _ in range(Y)]

dp[1][0] = 1
for i in range(1, Y):
  for j in range(1, X):
    if dp[j][i]:
      dp[i][j] = dp[j][i]
      continue
    dp[i][j] = (dp[i][j-1] + dp[i-1][j]) % MOD

print(dp[Y-1][X-1])

Fixed submission:
import math

MOD = 10**9 + 7

# nCk
def comb(n, r):
    r = min(r, n-r)
    if r == 0: return 1
    if r == 1: return n

    numerator = [n - r + k + 1 for k in range(r)]
    denominator = [k + 1 for k 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 *= int(numerator[k])

    return result
  
# nCk mod
def comb_mod(n, r, mod):
  r = min(r, n-r)
  
  g1 = [1, 1] # 元
  g2 = [1, 1] # 逆元
  inverse = [0, 1] # 逆元計算用
  
  for i in range(2, n+1):
    g1.append( (g1[-1] * i) % mod )
    inverse.append( (-inverse[mod % i] * (mod // i)) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

  return g1[n] * g2[r] * g2[n-r] % mod

X, Y = map(int, input().split())
  
if (X+Y)%3!=0:
  print(0)
  quit()

# (+1,+2):n, (+2,+1):m
m = (X*2 - Y) // 3
n = X - m*2

if m < 0 or n < 0:
  print(0)
  quit()

ans = comb_mod(n+m, n, MOD)

print(ans)

Buggy python submission (verdict: Runtime Error):
MOD = 10**9 + 7
X, Y = map(int, input().split())
  
if (X+Y)%3!=0:
  print(0)
  quit()
  
if X < Y:
  X, Y = Y, X

sub = X - Y
tan = Y - sub

X = sub + tan//3 + 3
Y = tan//3 + 3
dp = [[0]*X for _ in range(Y)]

dp[2][1] = 1
for i in range(2, Y):
  for j in range(2, X):
    dp[i][j] = (dp[i][j-1] + dp[i-1][j]) % MOD

print(dp[Y-1][X-1])

Fixed submission:
import math

MOD = 10**9 + 7

# nCk
def comb(n, r):
    r = min(r, n-r)
    if r == 0: return 1
    if r == 1: return n

    numerator = [n - r + k + 1 for k in range(r)]
    denominator = [k + 1 for k 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 *= int(numerator[k])

    return result
  
# nCk mod
def comb_mod(n, r, mod):
  r = min(r, n-r)
  
  g1 = [1, 1] # 元
  g2 = [1, 1] # 逆元
  inverse = [0, 1] # 逆元計算用
  
  for i in range(2, n+1):
    g1.append( (g1[-1] * i) % mod )
    inverse.append( (-inverse[mod % i] * (mod // i)) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

  return g1[n] * g2[r] * g2[n-r] % mod

X, Y = map(int, input().split())
  
if (X+Y)%3!=0:
  print(0)
  quit()

# (+1,+2):n, (+2,+1):m
m = (X*2 - Y) // 3
n = X - m*2

if m < 0 or n < 0:
  print(0)
  quit()

ans = comb_mod(n+m, n, MOD)

print(ans)

Buggy python submission (verdict: Runtime Error):
def solve():
  MOD = 10**9 + 7
  X, Y = map(int, input().split())
  
  if (X+Y)%3!=0:
    print(0)
    quit()
  
  if X < Y:
    X, Y = Y, X

  sub = X - Y
  tan = X - sub

  X = sub + tan + 1
  Y = tan + 1
  dp = [[0]*X for _ in range(Y)]

  dp[2][1] = 1
  for i in range(2, Y):
    for j in range(2, X):
      dp[i][j] = dp[i][j-1] + dp[i-1][j]

  dp[i][j] %= MOD

  #print(*dp, sep='\n')
  print(dp[Y-1][X-1])

if __name__ == '__main__':
  solve()

Fixed submission:
import math

MOD = 10**9 + 7

# nCk
def comb(n, r):
    r = min(r, n-r)
    if r == 0: return 1
    if r == 1: return n

    numerator = [n - r + k + 1 for k in range(r)]
    denominator = [k + 1 for k 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 *= int(numerator[k])

    return result
  
# nCk mod
def comb_mod(n, r, mod):
  r = min(r, n-r)
  
  g1 = [1, 1] # 元
  g2 = [1, 1] # 逆元
  inverse = [0, 1] # 逆元計算用
  
  for i in range(2, n+1):
    g1.append( (g1[-1] * i) % mod )
    inverse.append( (-inverse[mod % i] * (mod // i)) % mod )
    g2.append( (g2[-1] * inverse[-1]) % mod )

  return g1[n] * g2[r] * g2[n-r] % mod

X, Y = map(int, input().split())
  
if (X+Y)%3!=0:
  print(0)
  quit()

# (+1,+2):n, (+2,+1):m
m = (X*2 - Y) // 3
n = X - m*2

if m < 0 or n < 0:
  print(0)
  quit()

ans = comb_mod(n+m, n, MOD)

print(ans)