Buggy python submission (verdict: Runtime Error):
class Combination(object):
        """参考: https://harigami.net/contents?id=5f169f85-5707-4137-87a5-f0068749d9bb"""
        __slots__ = ['mod', 'factorial', 'inverse']

        def __init__(self, max_val_arg: int = 10**6, mod: int = 10**9 + 7):
            fac, inv = [1], []
            fac_append, inv_append = fac.append, inv.append

            for i in range(1, max_val_arg + 1):
                fac_append(fac[-1] * i % mod)

            inv_append(pow(fac[-1], mod - 2, mod))

            for i in range(max_val_arg, 0, -1):
                inv_append((inv[-1] * i) % mod)

            self.mod, self.factorial, self.inverse = mod, fac, inv[::-1]

        def combination(self, n, r):
            if n < 0 or r < 0 or n < r:
                return 0
            return self.factorial[n] * self.inverse[r] * self.inverse[n - r] % self.mod

if not S%3==0:
    print(0)
    exit()
else:
    small = S//3
    s_elm = min(X,Y)
    if s_elm<small:
        print(0)
        exit()
    r = s_elm - small
    ans = Combination().combination(small, r)
    ans %= u
print(ans)

Fixed submission:

import sys,itertools
def input():
    return sys.stdin.readline()[:-1]

X,Y = map(int,input().split(' '))
u = 10**9+7

S = X+Y

class Combination(object):
        """参考: https://harigami.net/contents?id=5f169f85-5707-4137-87a5-f0068749d9bb"""
        __slots__ = ['mod', 'factorial', 'inverse']

        def __init__(self, max_val_arg: int = 10**6, mod: int = 10**9 + 7):
            fac, inv = [1], []
            fac_append, inv_append = fac.append, inv.append

            for i in range(1, max_val_arg + 1):
                fac_append(fac[-1] * i % mod)

            inv_append(pow(fac[-1], mod - 2, mod))

            for i in range(max_val_arg, 0, -1):
                inv_append((inv[-1] * i) % mod)

            self.mod, self.factorial, self.inverse = mod, fac, inv[::-1]

        def combination(self, n, r):
            if n < 0 or r < 0 or n < r:
                return 0
            return self.factorial[n] * self.inverse[r] * self.inverse[n - r] % self.mod

if not S%3==0:
    print(0)
    exit()
else:
    small = S//3
    s_elm = min(X,Y)
    if s_elm<small:
        print(0)
        exit()
    r = s_elm - small
    ans = Combination().combination(small, r)
    ans %= u
print(ans)

Buggy python submission (verdict: Runtime Error):
class Combination(object):
        """参考: https://harigami.net/contents?id=5f169f85-5707-4137-87a5-f0068749d9bb"""
        __slots__ = ['mod', 'factorial', 'inverse']

        def __init__(self, max_val_arg: int = 10**6, mod: int = 10**9 + 7):
            fac, inv = [1], []
            fac_append, inv_append = fac.append, inv.append

            for i in range(1, max_val_arg + 1):
                fac_append(fac[-1] * i % mod)

            inv_append(pow(fac[-1], mod - 2, mod))

            for i in range(max_val_arg, 0, -1):
                inv_append((inv[-1] * i) % mod)

            self.mod, self.factorial, self.inverse = mod, fac, inv[::-1]

        def combination(self, n, r):
            if n < 0 or r < 0 or n < r:
                return 0
            return self.factorial[n] * self.inverse[r] * self.inverse[n - r] % self.mod

if not S%3==0:
    print(0)
    exit()
else:
    small = S//3
    s_elm = min(X,Y)
    if s_elm<small:
        print(0)
        exit()
    print('a')
    r = s_elm - small
    print(small,r)
    ans = Combination().combination(small, r)
    ans %= u
print(ans)

Fixed submission:

import sys,itertools
def input():
    return sys.stdin.readline()[:-1]

X,Y = map(int,input().split(' '))
u = 10**9+7

S = X+Y

class Combination(object):
        """参考: https://harigami.net/contents?id=5f169f85-5707-4137-87a5-f0068749d9bb"""
        __slots__ = ['mod', 'factorial', 'inverse']

        def __init__(self, max_val_arg: int = 10**6, mod: int = 10**9 + 7):
            fac, inv = [1], []
            fac_append, inv_append = fac.append, inv.append

            for i in range(1, max_val_arg + 1):
                fac_append(fac[-1] * i % mod)

            inv_append(pow(fac[-1], mod - 2, mod))

            for i in range(max_val_arg, 0, -1):
                inv_append((inv[-1] * i) % mod)

            self.mod, self.factorial, self.inverse = mod, fac, inv[::-1]

        def combination(self, n, r):
            if n < 0 or r < 0 or n < r:
                return 0
            return self.factorial[n] * self.inverse[r] * self.inverse[n - r] % self.mod

if not S%3==0:
    print(0)
    exit()
else:
    small = S//3
    s_elm = min(X,Y)
    if s_elm<small:
        print(0)
        exit()
    r = s_elm - small
    ans = Combination().combination(small, r)
    ans %= u
print(ans)