Buggy python submission (verdict: Time Limit Exceeded):
import math

def comb(n, k, m):
  nf  = math.factorial(n)   % m
  kf  = math.factorial(k)   % m
  nkf = math.factorial(n-k) % m
  return nf * pow_mod(kf*nkf%m, m-2, m) % m

def pow_mod(a, b, m):
  if b == 0:
    return 1
  elif b%2 == 0:
    d = pow_mod(a, b//2, m) % m
    return d * d % m 
  else:
    d = pow_mod(a, (b-1)//2, m)
    return  d * d * a % m

tmp = list(map(int, input().split()))
x = tmp[0]
y = tmp[1]

ans = 0
mod = 10**9 + 7

if (x + y) % 3 != 0:
  ans = 0
else:
  n = (x + y) // 3
  if min(x, y) < n:
    ans = 0
  elif min(x,y) == n:
    ans = 1
  else:
    r = min(x, y) - n
    ans = comb(n, r, mod)

print(ans)

Fixed submission:
import math

def comb(n, k, m):
  f = [1] * (n+1)
  for i in range(1, n+1):
    f[i] = f[i-1] * i % m
  return f[n] * pow_mod(f[k]*f[n-k]%m, m-2, m) % m

def pow_mod(a, b, m):
  if b == 0:
    return 1
  elif b%2 == 0:
    d = pow_mod(a, b//2, m) % m
    return d * d % m 
  else:
    d = pow_mod(a, (b-1)//2, m)
    return  d * d * a % m

tmp = list(map(int, input().split()))
x = tmp[0]
y = tmp[1]

ans = 0
mod = 10**9 + 7

if (x + y) % 3 != 0:
  ans = 0
else:
  n = (x + y) // 3
  if min(x, y) < n:
    ans = 0
  elif min(x,y) == n:
    ans = 1
  else:
    r = min(x, y) - n
    ans = comb(n, r, mod)

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import math

def comb(n, k, m):
  nf  = math.factorial(n)   % m
  kf  = math.factorial(k)   % m
  nkf = math.factorial(n-k) % m
  return nf * pow_mod(kf*nkf%m, m-2, m) % m

def pow_mod(a, b, m):
  if b == 0:
    return 1
  elif b%2 == 0:
    d = pow_mod(a, b//2, m) % m
    return d * d % m 
  else:
    d = pow_mod(a, (b-1)//2, m)
    return  d * d * a % m

tmp = list(map(int, input().split()))
x = tmp[0]
y = tmp[1]

ans = 0
mod = 10**9 + 7

if (x + y) % 3 != 0:
  ans = 0
else:
  n = (x + y) // 3
  if min(x, y) < n:
    ans = 0
  elif min(x,y) == n:
    ans = 1
  else:
    r = min(x, y) - n
    ans = comb(n, r, mod)

print(ans)

Fixed submission:
import math

def comb(n, k, m):
  f = [1] * (n+1)
  for i in range(1, n+1):
    f[i] = f[i-1] * i % m
  return f[n] * pow_mod(f[k]*f[n-k]%m, m-2, m) % m

def pow_mod(a, b, m):
  if b == 0:
    return 1
  elif b%2 == 0:
    d = pow_mod(a, b//2, m) % m
    return d * d % m 
  else:
    d = pow_mod(a, (b-1)//2, m)
    return  d * d * a % m

tmp = list(map(int, input().split()))
x = tmp[0]
y = tmp[1]

ans = 0
mod = 10**9 + 7

if (x + y) % 3 != 0:
  ans = 0
else:
  n = (x + y) // 3
  if min(x, y) < n:
    ans = 0
  elif min(x,y) == n:
    ans = 1
  else:
    r = min(x, y) - n
    ans = comb(n, r, mod)

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import math

def comb(n, k, m):
  nf  = math.factorial(n)   % m
  kf  = math.factorial(k)   % m
  nkf = math.factorial(n-k) % m
  return nf * pow_mod(kf*nkf%m, m-2, m) % m

def pow_mod(a, b, m):
  if b == 0:
    return 1
  elif b%2 == 0:
    return pow_mod(a, b//2, m) ** 2 % m 
  else:
    return pow_mod(a, b-1, m) * a % m

tmp = list(map(int, input().split()))
x = tmp[0]
y = tmp[1]

ans = 0
mod = 10**9 + 7

if (x + y) % 3 != 0:
  ans = 0
else:
  n = (x + y) // 3
  if min(x, y) < n:
    ans = 0
  elif min(x,y) == n:
    ans = 1
  else:
    r = min(x, y) - n
    ans = comb(n, r, mod)

print(ans)

Fixed submission:
import math

def comb(n, k, m):
  f = [1] * (n+1)
  for i in range(1, n+1):
    f[i] = f[i-1] * i % m
  return f[n] * pow_mod(f[k]*f[n-k]%m, m-2, m) % m

def pow_mod(a, b, m):
  if b == 0:
    return 1
  elif b%2 == 0:
    d = pow_mod(a, b//2, m) % m
    return d * d % m 
  else:
    d = pow_mod(a, (b-1)//2, m)
    return  d * d * a % m

tmp = list(map(int, input().split()))
x = tmp[0]
y = tmp[1]

ans = 0
mod = 10**9 + 7

if (x + y) % 3 != 0:
  ans = 0
else:
  n = (x + y) // 3
  if min(x, y) < n:
    ans = 0
  elif min(x,y) == n:
    ans = 1
  else:
    r = min(x, y) - n
    ans = comb(n, r, mod)

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import math

def comb(n, k, m):
  nf  = math.factorial(n)   % m
  kf  = math.factorial(k)   % m
  nkf = math.factorial(n-k) % m
  return nf * pow_mod(kf, m-2, m) * pow_mod(nkf, m-2, m) % m

def pow_mod(a, b, m):
  if b == 0:
    return 1
  elif b%2 == 0:
    return pow_mod(a, b//2, m) ** 2 % m 
  else:
    return pow_mod(a, b-1, m) * a % m

tmp = list(map(int, input().split()))
x = tmp[0]
y = tmp[1]

ans = 0
mod = 10**9 + 7

if (x + y) % 3 != 0:
  ans = 0
else:
  n = (x + y) // 3
  if min(x, y) < n:
    ans = 0
  elif min(x,y) == n:
    ans = 1
  else:
    r = min(x, y) - n
    ans = comb(n, r, mod)

print(ans)

Fixed submission:
import math

def comb(n, k, m):
  f = [1] * (n+1)
  for i in range(1, n+1):
    f[i] = f[i-1] * i % m
  return f[n] * pow_mod(f[k]*f[n-k]%m, m-2, m) % m

def pow_mod(a, b, m):
  if b == 0:
    return 1
  elif b%2 == 0:
    d = pow_mod(a, b//2, m) % m
    return d * d % m 
  else:
    d = pow_mod(a, (b-1)//2, m)
    return  d * d * a % m

tmp = list(map(int, input().split()))
x = tmp[0]
y = tmp[1]

ans = 0
mod = 10**9 + 7

if (x + y) % 3 != 0:
  ans = 0
else:
  n = (x + y) // 3
  if min(x, y) < n:
    ans = 0
  elif min(x,y) == n:
    ans = 1
  else:
    r = min(x, y) - n
    ans = comb(n, r, mod)

print(ans)

Buggy python submission (verdict: Time Limit Exceeded):
import sys
sys.setrecursionlimit(10**5)

def co (i, j):
  if i == 0 or j == 0:
    return 1
  else:
    return (co(i-1, j) + co(i, j-1)) % (10**9+7) 

tmp = list(map(int, input().split()))
x = tmp[0]
y = tmp[1]

ans = 0

if (x + y) % 3 != 0:
  ans = 0
else:
  mp = (x + y) // 3
  if min(x, y) < mp:
    ans = 0
  else:
    xi = x - mp
    yi = y - mp
    ans = co(xi, yi)

print(ans)

Fixed submission:
import math

def comb(n, k, m):
  f = [1] * (n+1)
  for i in range(1, n+1):
    f[i] = f[i-1] * i % m
  return f[n] * pow_mod(f[k]*f[n-k]%m, m-2, m) % m

def pow_mod(a, b, m):
  if b == 0:
    return 1
  elif b%2 == 0:
    d = pow_mod(a, b//2, m) % m
    return d * d % m 
  else:
    d = pow_mod(a, (b-1)//2, m)
    return  d * d * a % m

tmp = list(map(int, input().split()))
x = tmp[0]
y = tmp[1]

ans = 0
mod = 10**9 + 7

if (x + y) % 3 != 0:
  ans = 0
else:
  n = (x + y) // 3
  if min(x, y) < n:
    ans = 0
  elif min(x,y) == n:
    ans = 1
  else:
    r = min(x, y) - n
    ans = comb(n, r, mod)

print(ans)