Buggy python submission (verdict: Runtime Error):
import subprocess
import os
import time


import sys
import math
from copy import deepcopy
from collections import deque, defaultdict
from operator import mul
from functools import reduce
sys.setrecursionlimit(20000000)

input = sys.stdin.readline


mod = 10**9+7
N = 10**6
g1 = [1, 1]
g2 = [1, 1]
inverse = [0, 1]


def find_n(x, y):
    moves = int((x+y)/3)
    for n in range(moves+1):
        if n + (moves-n)*2 == x and n*2 + (moves-n) == y:
            return n % mod, (moves-n) % mod


# def cmb(n, r):
#     return math.factorial(n) % mod // ((math.factorial(r) % mod) * (math.factorial(n-r) % mod))


def cmb(n, r):
    if r < 0 or r > n:
        return 0
    r = min(r, n-r)

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


def main():
    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)

    x, y = map(int, input().split())

    if (x+y) % 3:
        print(0)
        sys.exit()

    n, m = find_n(x, y)

    # n = int(((x*2 - y) // 3))
    # m = int(((y*2 - x) // 3))

    ans = cmb(n+m, n)

    print(ans)


if __name__ == '__main__':
    main()


Fixed submission:
import subprocess
import os
import time


import sys
import math
from copy import deepcopy
from collections import deque, defaultdict
from operator import mul
from functools import reduce
sys.setrecursionlimit(20000000)

input = sys.stdin.readline


mod = 10**9+7
N = 10**6
g1 = [1, 1]
g2 = [1, 1]
inverse = [0, 1]


# def find_n(x, y):
#     moves = int((x+y)/3)
#     for n in range(moves+1):
#         if n + (moves-n)*2 == x and n*2 + (moves-n) == y:
#             return n % mod, (moves-n) % mod


# def cmb(n, r):
#     return math.factorial(n) % mod // ((math.factorial(r) % mod) * (math.factorial(n-r) % mod))


def cmb(n, r):
    if r < 0 or r > n:
        return 0
    r = min(r, n-r)

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


def main():
    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)

    x, y = map(int, input().split())

    if (x+y) % 3:
        print(0)
        sys.exit()

    # n, m = find_n(x, y)

    n = int(((x*2 - y) // 3))
    m = int(((y*2 - x) // 3))

    ans = cmb(n+m, n)

    print(ans)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
import subprocess
import os
import time


import sys
import math
from copy import deepcopy
from collections import deque, defaultdict
from operator import mul
from functools import reduce
sys.setrecursionlimit(20000000)

input = sys.stdin.readline


mod = 10**9+7
N = 10**6 + 500000
g1 = [1, 1]
g2 = [1, 1]
inverse = [0, 1]


# def find_n(x, y):
#     moves = int((x+y)/3)
#     for n in range(moves+1):
#         if n + (moves-n)*2 == x and n*2 + (moves-n) == y:
#             return n % mod, (moves-n) % mod


# def cmb(n, r):
#     return math.factorial(n) % mod // ((math.factorial(r) % mod) * (math.factorial(n-r) % mod))


def cmb(n, r):
    if r < 0 or r > n:
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod


def main():
    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)

    x, y = map(int, input().split())

    if (x+y) % 3:
        print(0)
        sys.exit()

    # n, m = find_n(x, y)

    n = int(((x*2 - y) / 3)) % mod
    m = int(((y*2 - x) / 3)) % mod

    ans = cmb(n+m, n)

    print(ans)


if __name__ == '__main__':
    main()


Fixed submission:
import subprocess
import os
import time


import sys
import math
from copy import deepcopy
from collections import deque, defaultdict
from operator import mul
from functools import reduce
sys.setrecursionlimit(20000000)

input = sys.stdin.readline


mod = 10**9+7
N = 10**6
g1 = [1, 1]
g2 = [1, 1]
inverse = [0, 1]


# def find_n(x, y):
#     moves = int((x+y)/3)
#     for n in range(moves+1):
#         if n + (moves-n)*2 == x and n*2 + (moves-n) == y:
#             return n % mod, (moves-n) % mod


# def cmb(n, r):
#     return math.factorial(n) % mod // ((math.factorial(r) % mod) * (math.factorial(n-r) % mod))


def cmb(n, r):
    if r < 0 or r > n:
        return 0
    r = min(r, n-r)

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


def main():
    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)

    x, y = map(int, input().split())

    if (x+y) % 3:
        print(0)
        sys.exit()

    # n, m = find_n(x, y)

    n = int(((x*2 - y) // 3))
    m = int(((y*2 - x) // 3))

    ans = cmb(n+m, n)

    print(ans)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
import subprocess
import os
import time


import sys
import math
from copy import deepcopy
from collections import deque, defaultdict
from operator import mul
from functools import reduce
sys.setrecursionlimit(20000000)

input = sys.stdin.readline


mod = 10**9+7
N = 10**6
g1 = [1, 1]
g2 = [1, 1]
inverse = [0, 1]


# def find_n(x, y):
#     moves = int((x+y)/3)
#     for n in range(moves+1):
#         if n + (moves-n)*2 == x and n*2 + (moves-n) == y:
#             return n % mod, (moves-n) % mod


# def cmb(n, r):
#     return math.factorial(n) % mod // ((math.factorial(r) % mod) * (math.factorial(n-r) % mod))


def cmb(n, r):
    if r < 0 or r > n:
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod


def main():
    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)

    x, y = map(int, input().split())

    if (x+y) % 3:
        print(0)
        sys.exit()

    # n, m = find_n(x, y)

    n = int(((x*2 - y) / 3)) % mod
    m = int(((y*2 - x) / 3)) % mod

    ans = cmb(n+m, min([n, m]))

    print(ans)


if __name__ == '__main__':
    main()

Fixed submission:
import subprocess
import os
import time


import sys
import math
from copy import deepcopy
from collections import deque, defaultdict
from operator import mul
from functools import reduce
sys.setrecursionlimit(20000000)

input = sys.stdin.readline


mod = 10**9+7
N = 10**6
g1 = [1, 1]
g2 = [1, 1]
inverse = [0, 1]


# def find_n(x, y):
#     moves = int((x+y)/3)
#     for n in range(moves+1):
#         if n + (moves-n)*2 == x and n*2 + (moves-n) == y:
#             return n % mod, (moves-n) % mod


# def cmb(n, r):
#     return math.factorial(n) % mod // ((math.factorial(r) % mod) * (math.factorial(n-r) % mod))


def cmb(n, r):
    if r < 0 or r > n:
        return 0
    r = min(r, n-r)

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


def main():
    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)

    x, y = map(int, input().split())

    if (x+y) % 3:
        print(0)
        sys.exit()

    # n, m = find_n(x, y)

    n = int(((x*2 - y) // 3))
    m = int(((y*2 - x) // 3))

    ans = cmb(n+m, n)

    print(ans)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
import subprocess
import os
import time


import sys
import math
from copy import deepcopy
from collections import deque, defaultdict
from operator import mul
from functools import reduce
sys.setrecursionlimit(20000000)

input = sys.stdin.readline


mod = 10**9+7
N = 10**6
g1 = [1, 1]
g2 = [1, 1]
inverse = [0, 1]


def find_n(x, y):
    moves = int((x+y)/3)
    for n in range(moves+1):
        if n + (moves-n)*2 == x and n*2 + (moves-n) == y:
            return n, moves-n


# def cmb(n, r):
#     return math.factorial(n) % mod // ((math.factorial(r) % mod) * (math.factorial(n-r) % mod))


def cmb(n, r):
    if r < 0 or r > n:
        return 0
    r = min(r, n-r)
    return g1[n] * g2[r] * g2[n-r] % mod


def main():
    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)

    x, y = map(int, input().split())

    if (x+y) % 3:
        print(0)
        sys.exit()

    n, m = find_n(x, y)

    ans = cmb(n+m, min([n, m]))

    print(ans)


if __name__ == '__main__':
    main()


Fixed submission:
import subprocess
import os
import time


import sys
import math
from copy import deepcopy
from collections import deque, defaultdict
from operator import mul
from functools import reduce
sys.setrecursionlimit(20000000)

input = sys.stdin.readline


mod = 10**9+7
N = 10**6
g1 = [1, 1]
g2 = [1, 1]
inverse = [0, 1]


# def find_n(x, y):
#     moves = int((x+y)/3)
#     for n in range(moves+1):
#         if n + (moves-n)*2 == x and n*2 + (moves-n) == y:
#             return n % mod, (moves-n) % mod


# def cmb(n, r):
#     return math.factorial(n) % mod // ((math.factorial(r) % mod) * (math.factorial(n-r) % mod))


def cmb(n, r):
    if r < 0 or r > n:
        return 0
    r = min(r, n-r)

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


def main():
    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)

    x, y = map(int, input().split())

    if (x+y) % 3:
        print(0)
        sys.exit()

    # n, m = find_n(x, y)

    n = int(((x*2 - y) // 3))
    m = int(((y*2 - x) // 3))

    ans = cmb(n+m, n)

    print(ans)


if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
import subprocess
import os
import time


import sys
import math
from copy import deepcopy
from collections import deque, defaultdict
from operator import mul
from functools import reduce
sys.setrecursionlimit(20000000)

input = sys.stdin.readline


def find_n(x, y):
    moves = int((x+y)/3)
    for n in range(moves+1):
        if n + (moves-n)*2 == x and n*2 + (moves-n) == y:
            return n, moves-n


def cmb(n, m):
    return math.factorial(n+m) // (math.factorial(n+m - n) * math.factorial(n))


def main():
    x, y = map(int, input().split())

    if (x+y) % 3:
        print(0)
        sys.exit()

    n, m = find_n(x, y)

    ans = cmb(min([n, m]), max([n, m]))

    print(ans % (10**9 + 7))


if __name__ == '__main__':
    main()

Fixed submission:
import subprocess
import os
import time


import sys
import math
from copy import deepcopy
from collections import deque, defaultdict
from operator import mul
from functools import reduce
sys.setrecursionlimit(20000000)

input = sys.stdin.readline


mod = 10**9+7
N = 10**6
g1 = [1, 1]
g2 = [1, 1]
inverse = [0, 1]


# def find_n(x, y):
#     moves = int((x+y)/3)
#     for n in range(moves+1):
#         if n + (moves-n)*2 == x and n*2 + (moves-n) == y:
#             return n % mod, (moves-n) % mod


# def cmb(n, r):
#     return math.factorial(n) % mod // ((math.factorial(r) % mod) * (math.factorial(n-r) % mod))


def cmb(n, r):
    if r < 0 or r > n:
        return 0
    r = min(r, n-r)

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


def main():
    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)

    x, y = map(int, input().split())

    if (x+y) % 3:
        print(0)
        sys.exit()

    # n, m = find_n(x, y)

    n = int(((x*2 - y) // 3))
    m = int(((y*2 - x) // 3))

    ans = cmb(n+m, n)

    print(ans)


if __name__ == '__main__':
    main()