Buggy python submission (verdict: Time Limit Exceeded):
MOD = 10 ** 9 + 7

#互いに素なa,bについて、a*x+b*y=1の一つの解
def extgcd(a,b):
    r = [1,0,a]
    w = [0,1,b]
    while w[2]!=1:
        q = r[2]//w[2]
        r2 = w
        w2 = [r[0]-q*w[0],r[1]-q*w[1],r[2]-q*w[2]]
        r = r2
        w = w2
    #[x,y]
    return [w[0],w[1]]

# aの逆元(mod m)を求める。(aとmは互いに素であることが前提)
def mod_inv(a,m):
    x = extgcd(a,m)[0]
    return (m+x%m)%m

X, Y = map(int, input().split())
if (X + Y) % 3 != 0:
    print(0)
    exit()
time = (X+Y) // 3
diff = X - Y
if abs(diff) > time:
    print(0)
    exit()
x_time = (time+diff) // 2
res = 1
for i in range(1,time+1):
    res = res*i%MOD
for i in range(1,x_time+1):
    res = res*mod_inv(i,MOD)%MOD
for i in range(1,time-x_time+1):
    res = res*mod_inv(i, MOD)%MOD
print(res)
#print(mod_combination(time, x_time, MOD))


Fixed submission:
import numpy as np
from math import factorial
MOD = 10 ** 9 + 7

def cumprod(arr,MOD):
    L = len(arr); Lsq = int(L**.5+1)
    arr = np.resize(arr,Lsq**2).reshape(Lsq,Lsq)
    for n in range(1,Lsq):
        arr[:,n] *= arr[:,n-1]; arr[:,n] %= MOD
    for n in range(1,Lsq):
        arr[n] *= arr[n-1,-1]; arr[n] %= MOD
    return arr.ravel()[:L]

def make_fact(U,MOD):
    x = np.arange(U,dtype=np.int64); x[0] = 1
    fact = cumprod(x,MOD)
    x = np.arange(U,0,-1,dtype=np.int64); x[0] = pow(int(fact[-1]),MOD-2,MOD)
    fact_inv = cumprod(x,MOD)[::-1]
    return fact,fact_inv



U = 10**6
fact, fact_inv = make_fact(U,MOD)

X, Y = map(int, input().split())
if (X + Y) % 3 != 0:
    print(0)
    exit()
time = (X+Y) // 3
diff = X - Y
if abs(diff) > time:
    print(0)
    exit()
x_time = (time+diff) // 2

answer = fact[time] * fact_inv[x_time] % MOD * fact_inv[time-x_time] % MOD
print(answer)

Buggy python submission (verdict: Time Limit Exceeded):
from math import factorial
MOD = 10 ** 9 + 7

#互いに素なa,bについて、a*x+b*y=1の一つの解
def extgcd(a,b):
    r = [1,0,a]
    w = [0,1,b]
    while w[2]!=1:
        q = r[2]//w[2]
        r2 = w
        w2 = [r[0]-q*w[0],r[1]-q*w[1],r[2]-q*w[2]]
        r = r2
        w = w2
    #[x,y]
    return [w[0],w[1]]

# aの逆元(mod m)を求める。(aとmは互いに素であることが前提)
def mod_inv(a,m):
    x = extgcd(a,m)[0]
    return (m+x%m)%m

X, Y = map(int, input().split())
if (X + Y) % 3 != 0:
    print(0)
    exit()
time = (X+Y) // 3
diff = X - Y
if abs(diff) > time:
    print(0)
    exit()
x_time = (time+diff) // 2
res = 1
for i in range(1,time+1):
    res = res*i%MOD
for i in range(1,x_time+1):
    res = res*mod_inv(i,MOD)%MOD
for i in range(1,time-x_time+1):
    res = res*mod_inv(i, MOD)%MOD
print(res)
#print(mod_combination(time, x_time, MOD))


Fixed submission:
import numpy as np
from math import factorial
MOD = 10 ** 9 + 7

def cumprod(arr,MOD):
    L = len(arr); Lsq = int(L**.5+1)
    arr = np.resize(arr,Lsq**2).reshape(Lsq,Lsq)
    for n in range(1,Lsq):
        arr[:,n] *= arr[:,n-1]; arr[:,n] %= MOD
    for n in range(1,Lsq):
        arr[n] *= arr[n-1,-1]; arr[n] %= MOD
    return arr.ravel()[:L]

def make_fact(U,MOD):
    x = np.arange(U,dtype=np.int64); x[0] = 1
    fact = cumprod(x,MOD)
    x = np.arange(U,0,-1,dtype=np.int64); x[0] = pow(int(fact[-1]),MOD-2,MOD)
    fact_inv = cumprod(x,MOD)[::-1]
    return fact,fact_inv



U = 10**6
fact, fact_inv = make_fact(U,MOD)

X, Y = map(int, input().split())
if (X + Y) % 3 != 0:
    print(0)
    exit()
time = (X+Y) // 3
diff = X - Y
if abs(diff) > time:
    print(0)
    exit()
x_time = (time+diff) // 2

answer = fact[time] * fact_inv[x_time] % MOD * fact_inv[time-x_time] % MOD
print(answer)