Buggy python submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
import math

MOD = 10**9+7  # type: int

def combi_count(n, r):
    x = 1
    y = 1
    for i in range(1, r+1):
        x *= (n-i) % MOD
        y *= i % MOD

    # nCr = n!/((n-r)!*r!) = (n!/(n-r)!) / r! 
    #     :=                 (    x    ) / y

    # x / y            % MOD
    # x * y^(-1)       % MOD
    # x * y**(MOD - 2) % MOD (from フェルマー定理)

    return x * pow(y, MOD-2, MOD) % MOD

def solve(X: int, Y: int):
    a = int((2*Y - X)/3)
    b = int((2*X - Y)/3)
    if ((2*Y - X)%3 != 0) and ((2*X - Y)%3 != 0):
        ans = 0
    else:
        if (a<0) or (b<0):
            ans = 0
        else:
            ans = combi_count(a+b, min(a, b))
    print(int(ans%MOD))

# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    X = int(next(tokens))  # type: int
    Y = int(next(tokens))  # type: int
    solve(X, Y)

if __name__ == '__main__':
    main()
atcoder-tools: The pre-rendered templates are not found.

Fixed submission:
#!/usr/bin/env python3
import sys
import math

MOD = 10**9+7  # type: int

def combi_count(n, r):
    x = 1
    y = 1
    for i in range(1, r+1):
        x = x * (n-i) % MOD
        y = y * i % MOD

    # nCr = n!/((n-r)!*r!) = (n!/(n-r)!) / r! 
    #     :=                 (    x    ) / y

    # x / y            % MOD
    # x * y^(-1)       % MOD
    # x * y**(MOD - 2) % MOD (from フェルマー定理)

    return x * pow(y, MOD-2, MOD) % MOD

def solve(X: int, Y: int):
    a = int((2*Y - X)/3)
    b = int((2*X - Y)/3)
    if ( ((2*Y - X)%3 != 0) and ((2*X - Y)%3 != 0) )  or ((a<0) or (b<0)):
        ans = 0
    else:
        ans = combi_count(a+b+1, min(a, b))
    print(ans)

# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    X, Y = map(int, input().split())
    solve(X, Y)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
import math

MOD = 10**9+7  # type: int

def combi_count(n, r):
    x = 1
    y = 1
    for i in range(1, r+1):
        x *= (n-i) % MOD
        y *= i % MOD

    # nCr = n!/((n-r)!*r!) = (n!/(n-r)!) / r! 
    #     :=                 (    x    ) / y
    
    # x / y            % MOD
    # x * y^(-1)       % MOD
    # x * y**(MOD - 2) % MOD (from フェルマー定理)

    return x * pow(y, MOD-2, MOD) % MOD

def solve(X: int, Y: int):
    a = (2*Y - X)/3
    b = (2*X - Y)/3
    if ((2*Y - X)%3 != 0) and ((2*X - Y)%3 != 0):
        ans = 0
    else:
        if (a<0) or (b<0):
            ans = 0
        else:
            ans = combi_count(a+b, min(a, b))
    print(int(ans%MOD))

# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    X = int(next(tokens))  # type: int
    Y = int(next(tokens))  # type: int
    solve(X, Y)

if __name__ == '__main__':
    main()

Fixed submission:
#!/usr/bin/env python3
import sys
import math

MOD = 10**9+7  # type: int

def combi_count(n, r):
    x = 1
    y = 1
    for i in range(1, r+1):
        x = x * (n-i) % MOD
        y = y * i % MOD

    # nCr = n!/((n-r)!*r!) = (n!/(n-r)!) / r! 
    #     :=                 (    x    ) / y

    # x / y            % MOD
    # x * y^(-1)       % MOD
    # x * y**(MOD - 2) % MOD (from フェルマー定理)

    return x * pow(y, MOD-2, MOD) % MOD

def solve(X: int, Y: int):
    a = int((2*Y - X)/3)
    b = int((2*X - Y)/3)
    if ( ((2*Y - X)%3 != 0) and ((2*X - Y)%3 != 0) )  or ((a<0) or (b<0)):
        ans = 0
    else:
        ans = combi_count(a+b+1, min(a, b))
    print(ans)

# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    X, Y = map(int, input().split())
    solve(X, Y)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Time Limit Exceeded):
#!/usr/bin/env python3
import sys
import math

MOD = 10**9+7  # type: int

def combi_count(n, r):
    return math.factorial(int(n)) // (math.factorial(int(r)) * math.factorial(int(n - r)))

def solve(X: int, Y: int):
    a = (2*Y - X)/3
    b = (2*X - Y)/3
    if ((2*Y - X)%3 != 0) and ((2*X - Y)%3 != 0):
        ans = 0
    else:
        if (a<0) or (b<0):
            ans = 0
        else:
            ans = combi_count(a+b, min(a, b))
    print(int(ans%MOD))

# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    X = int(next(tokens))  # type: int
    Y = int(next(tokens))  # type: int
    solve(X, Y)

if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys
import math

MOD = 10**9+7  # type: int

def combi_count(n, r):
    x = 1
    y = 1
    for i in range(1, r+1):
        x = x * (n-i) % MOD
        y = y * i % MOD

    # nCr = n!/((n-r)!*r!) = (n!/(n-r)!) / r! 
    #     :=                 (    x    ) / y

    # x / y            % MOD
    # x * y^(-1)       % MOD
    # x * y**(MOD - 2) % MOD (from フェルマー定理)

    return x * pow(y, MOD-2, MOD) % MOD

def solve(X: int, Y: int):
    a = int((2*Y - X)/3)
    b = int((2*X - Y)/3)
    if ( ((2*Y - X)%3 != 0) and ((2*X - Y)%3 != 0) )  or ((a<0) or (b<0)):
        ans = 0
    else:
        ans = combi_count(a+b+1, min(a, b))
    print(ans)

# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    X, Y = map(int, input().split())
    solve(X, Y)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
atcoder-tools: The pre-rendered templates are not found.

Fixed submission:
#!/usr/bin/env python3
import sys
import math

MOD = 10**9+7  # type: int

def combi_count(n, r):
    x = 1
    y = 1
    for i in range(1, r+1):
        x = x * (n-i) % MOD
        y = y * i % MOD

    # nCr = n!/((n-r)!*r!) = (n!/(n-r)!) / r! 
    #     :=                 (    x    ) / y

    # x / y            % MOD
    # x * y^(-1)       % MOD
    # x * y**(MOD - 2) % MOD (from フェルマー定理)

    return x * pow(y, MOD-2, MOD) % MOD

def solve(X: int, Y: int):
    a = int((2*Y - X)/3)
    b = int((2*X - Y)/3)
    if ( ((2*Y - X)%3 != 0) and ((2*X - Y)%3 != 0) )  or ((a<0) or (b<0)):
        ans = 0
    else:
        ans = combi_count(a+b+1, min(a, b))
    print(ans)

# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    X, Y = map(int, input().split())
    solve(X, Y)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
import math

MOD = 10**9+7  # type: int

def solve(X: int, Y: int):
    a = (2*Y - X)/3
    b = (2*X - Y)/3
    if ((2*Y - X)%3 != 0) and ((2*X - Y)%3 != 0):
        ans = 0
    else:
        if a<0 or b<0:
            ans = 0
        else:
            factorial_ab = math.factorial(int(min(a, b)))
            ans = math.factorial(int(a+b)) / factorial_ab
    print(int(ans%MOD))

# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    X = int(next(tokens))  # type: int
    Y = int(next(tokens))  # type: int
    solve(X, Y)

if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys
import math

MOD = 10**9+7  # type: int

def combi_count(n, r):
    x = 1
    y = 1
    for i in range(1, r+1):
        x = x * (n-i) % MOD
        y = y * i % MOD

    # nCr = n!/((n-r)!*r!) = (n!/(n-r)!) / r! 
    #     :=                 (    x    ) / y

    # x / y            % MOD
    # x * y^(-1)       % MOD
    # x * y**(MOD - 2) % MOD (from フェルマー定理)

    return x * pow(y, MOD-2, MOD) % MOD

def solve(X: int, Y: int):
    a = int((2*Y - X)/3)
    b = int((2*X - Y)/3)
    if ( ((2*Y - X)%3 != 0) and ((2*X - Y)%3 != 0) )  or ((a<0) or (b<0)):
        ans = 0
    else:
        ans = combi_count(a+b+1, min(a, b))
    print(ans)

# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    X, Y = map(int, input().split())
    solve(X, Y)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
import math

MOD = 10**9+7  # type: int

def solve(X: int, Y: int):
    a = (2*Y - X)/3
    b = (2*X - Y)/3
    if ((2*Y - X)%3 != 0) and ((2*X - Y)%3 != 0):
        ans = 0
    else:
        if (a<0) or (b<0):
            ans = 0
        else:
            factorial_ab = math.factorial(int(min(a, b)))
            ans = math.factorial(int(a+b)) / factorial_ab
    print(int(ans%MOD))

# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    X = int(next(tokens))  # type: int
    Y = int(next(tokens))  # type: int
    solve(X, Y)

if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys
import math

MOD = 10**9+7  # type: int

def combi_count(n, r):
    x = 1
    y = 1
    for i in range(1, r+1):
        x = x * (n-i) % MOD
        y = y * i % MOD

    # nCr = n!/((n-r)!*r!) = (n!/(n-r)!) / r! 
    #     :=                 (    x    ) / y

    # x / y            % MOD
    # x * y^(-1)       % MOD
    # x * y**(MOD - 2) % MOD (from フェルマー定理)

    return x * pow(y, MOD-2, MOD) % MOD

def solve(X: int, Y: int):
    a = int((2*Y - X)/3)
    b = int((2*X - Y)/3)
    if ( ((2*Y - X)%3 != 0) and ((2*X - Y)%3 != 0) )  or ((a<0) or (b<0)):
        ans = 0
    else:
        ans = combi_count(a+b+1, min(a, b))
    print(ans)

# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    X, Y = map(int, input().split())
    solve(X, Y)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
import math

MOD = 1000000007  # type: int

def solve(X: int, Y: int):
    a = (2*Y - X)/3
    b = (2*X - Y)/3
    if ((2*Y - X)%3 != 0) and ((2*X - Y)%3 != 0):
        ans = 0
    else:
        if (a<0) or (b<0):
            ans = 0
        else:
            factorial_ab = math.factorial(int(min(a, b)))
            ans = math.factorial(int(a+b)) / factorial_ab
    print(int(ans%MOD))

# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    X = int(next(tokens))  # type: int
    Y = int(next(tokens))  # type: int
    solve(X, Y)

if __name__ == '__main__':
    main()

Fixed submission:
#!/usr/bin/env python3
import sys
import math

MOD = 10**9+7  # type: int

def combi_count(n, r):
    x = 1
    y = 1
    for i in range(1, r+1):
        x = x * (n-i) % MOD
        y = y * i % MOD

    # nCr = n!/((n-r)!*r!) = (n!/(n-r)!) / r! 
    #     :=                 (    x    ) / y

    # x / y            % MOD
    # x * y^(-1)       % MOD
    # x * y**(MOD - 2) % MOD (from フェルマー定理)

    return x * pow(y, MOD-2, MOD) % MOD

def solve(X: int, Y: int):
    a = int((2*Y - X)/3)
    b = int((2*X - Y)/3)
    if ( ((2*Y - X)%3 != 0) and ((2*X - Y)%3 != 0) )  or ((a<0) or (b<0)):
        ans = 0
    else:
        ans = combi_count(a+b+1, min(a, b))
    print(ans)

# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    X, Y = map(int, input().split())
    solve(X, Y)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
atcoder-tools: The pre-rendered templates are not found.

Fixed submission:
#!/usr/bin/env python3
import sys
import math

MOD = 10**9+7  # type: int

def combi_count(n, r):
    x = 1
    y = 1
    for i in range(1, r+1):
        x = x * (n-i) % MOD
        y = y * i % MOD

    # nCr = n!/((n-r)!*r!) = (n!/(n-r)!) / r! 
    #     :=                 (    x    ) / y

    # x / y            % MOD
    # x * y^(-1)       % MOD
    # x * y**(MOD - 2) % MOD (from フェルマー定理)

    return x * pow(y, MOD-2, MOD) % MOD

def solve(X: int, Y: int):
    a = int((2*Y - X)/3)
    b = int((2*X - Y)/3)
    if ( ((2*Y - X)%3 != 0) and ((2*X - Y)%3 != 0) )  or ((a<0) or (b<0)):
        ans = 0
    else:
        ans = combi_count(a+b+1, min(a, b))
    print(ans)

# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    X, Y = map(int, input().split())
    solve(X, Y)

if __name__ == '__main__':
    main()

Buggy python submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
import math

MOD = 1000000007  # type: int

def solve(X: int, Y: int):
    a = (2*Y - X)/3
    b = (2*X - Y)/3
    if ((2*Y - X)%3 != 0) and ((2*X - Y)%3 != 0):
        ans = 0
    else:
        if (a<0) or (b<0):
            ans = 0
        else:
            f_a = math.factorial(int(a))
            if a==b:
                ans = math.factorial(int(a+b)) / f_a / f_a
            else:
                ans = math.factorial(int(a+b)) / f_a / math.factorial(int(b))
    print(int(ans%MOD))

def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    X = int(next(tokens))  # type: int
    Y = int(next(tokens))  # type: int
    solve(X, Y)

if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys
import math

MOD = 10**9+7  # type: int

def combi_count(n, r):
    x = 1
    y = 1
    for i in range(1, r+1):
        x = x * (n-i) % MOD
        y = y * i % MOD

    # nCr = n!/((n-r)!*r!) = (n!/(n-r)!) / r! 
    #     :=                 (    x    ) / y

    # x / y            % MOD
    # x * y^(-1)       % MOD
    # x * y**(MOD - 2) % MOD (from フェルマー定理)

    return x * pow(y, MOD-2, MOD) % MOD

def solve(X: int, Y: int):
    a = int((2*Y - X)/3)
    b = int((2*X - Y)/3)
    if ( ((2*Y - X)%3 != 0) and ((2*X - Y)%3 != 0) )  or ((a<0) or (b<0)):
        ans = 0
    else:
        ans = combi_count(a+b+1, min(a, b))
    print(ans)

# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    X, Y = map(int, input().split())
    solve(X, Y)

if __name__ == '__main__':
    main()