Buggy python submission (verdict: Runtime Error):
import sys
input = sys.stdin.readline

_x, _y = map(int, input().split())


def combination(n, r, mod=10 ** 9 + 7):
    n1, r = n + 1, min(r, n - r)
    numer = denom = 1
    for i in range(1, r + 1):
        numer = numer * (n1 - i) % mod
        denom = denom * i % mod
    return numer * pow(denom, mod - 2, mod) % mod


X, Y = map(int, input().split())
if (X + Y) % 3 != 0 or not (X <= 2 * Y and Y <= 2 * X):
    print(0)
    exit()

n = (X + Y) // 3
r = Y - n
print(combination(n, r))


def nCk(n, k, m=10 ** 9 + 7):
    a = b = 1
    k = min(k, n - k)
    for i in range(k):
        a = (a * (n - i)) % m
        b = (b * (i + 1)) % m

    return (a * pow(b, m - 2, m)) % m


def chker(x, y):
    if (x + y) % 3 != 0 or x > 2 * y or y > 2 * x:
        print(0)
        return

    if x == y:
        b = x // 3
        print(nCk(2 * b, b))
        return

    x, y = (x, y) if x < y else (y, x)

    b = 2 * x - y
    if b % 3 != 0:
        print(0)
        return

    d1, d2 = b // 3, x - 2 * (b // 3)
    u = d1 + d2

    print(nCk(u, d1))


chker(_x, _y)


Fixed submission:
import sys
input = sys.stdin.readline

_x, _y = map(int, input().split())


def nCk(n, k, m=10 ** 9 + 7):
    a = b = 1
    k = min(k, n - k)
    for i in range(k):
        a = (a * (n - i)) % m
        b = (b * (i + 1)) % m

    return (a * pow(b, m - 2, m)) % m


def chker(x, y):
    if (x + y) % 3 != 0 or x > 2 * y or y > 2 * x:
        print(0)
        return

    if x == y:
        b = x // 3
        print(nCk(2 * b, b))
        return

    x, y = (x, y) if x < y else (y, x)

    b = 2 * x - y
    if b % 3 != 0:
        print(0)
        return

    d1, d2 = b // 3, x - 2 * (b // 3)
    u = d1 + d2

    print(nCk(u, d1))


chker(_x, _y)

Buggy python submission (verdict: Runtime Error):
import sys
input = sys.stdin.readline

_x, _y = map(int, input().split())


def modinv(a, mod=10**9 + 7):
    return pow(a, mod - 2, mod)


def combination(n, r, mod=10**9 + 7):
    r = min(r, n - r)
    res = 1
    for i in range(r):
        res = res * (n - i) * modinv(i + 1, mod) % mod
    return res


def chker(x, y):
    if x == y:
        if x % 3 != 0:
            print(0)
            return

        b = x // 3
        print(combination(2 * b, b))
        return

    x, y = (x, y) if x > y else (y, x)

    b = y - x / 2
    if 2 * b % 3 != 0:
        print(0)
        return

    d1, d2 = 2 * b // 3, int(x / 2 - b / 3)
    u = d1 + d2

    print(combination(u, min(d1, d2)))


chker(_x, _y)


Fixed submission:
import sys
input = sys.stdin.readline

_x, _y = map(int, input().split())


def nCk(n, k, m=10 ** 9 + 7):
    a = b = 1
    k = min(k, n - k)
    for i in range(k):
        a = (a * (n - i)) % m
        b = (b * (i + 1)) % m

    return (a * pow(b, m - 2, m)) % m


def chker(x, y):
    if (x + y) % 3 != 0 or x > 2 * y or y > 2 * x:
        print(0)
        return

    if x == y:
        b = x // 3
        print(nCk(2 * b, b))
        return

    x, y = (x, y) if x < y else (y, x)

    b = 2 * x - y
    if b % 3 != 0:
        print(0)
        return

    d1, d2 = b // 3, x - 2 * (b // 3)
    u = d1 + d2

    print(nCk(u, d1))


chker(_x, _y)