Buggy python submission (verdict: Time Limit Exceeded):
import math


def digit_sum(b, n):
    if b > n:
        return n
    else:
        return digit_sum(b=b, n=n // b) + n % b


def main(n, s):
    if s > n:
        return -1
    elif n == s:
        return n + 1
    else:
        b = 2
        while b * b <= n:
            if digit_sum(b, n) == s:
                return b

        p = 1
        b_min = -1
        while p * p <= n:
            if (n - s) % p == 0:
                b = (n - s) // p + 1
                if digit_sum(b, n) == s:
                    b_min = min(b_min, b) if b_min != -1 else b
            p += 1
        return b_min


if __name__ == '__main__':
    N = int(input())
    S = int(input())
    print(main(n=N, s=S))


Fixed submission:
import math


def digit_sum(b, n):
    if b > n:
        return n
    else:
        return digit_sum(b=b, n=n // b) + n % b


def main(n, s):
    if s > n:
        return -1
    elif n == s:
        return n + 1
    else:
        b = 2
        while b * b <= n:
            if digit_sum(b, n) == s:
                return b
            b += 1

        p = 1
        b_min = -1
        while p * p <= n:
            if (n - s) % p == 0:
                b = (n - s) // p + 1
                if digit_sum(b, n) == s:
                    b_min = min(b_min, b) if b_min != -1 else b
            p += 1
        return b_min


if __name__ == '__main__':
    N = int(input())
    S = int(input())
    print(main(n=N, s=S))

Buggy python submission (verdict: Runtime Error):
import math


def digit_sum(b, n):
    if b > n:
        return n
    else:
        return digit_sum(b=b, n=n // b) + n % b


def main(n, s):
    if s > n:
        return -1
    elif n == s:
        return n + 1
    else:
        sqrt_n = int(math.sqrt(n))
        for b in range(2, sqrt_n + 1):
            if digit_sum(b, n) == s:
                return b
        b_min = 1L << 55
        for p in range(1, sqrt_n):
            if (n - s) % p == 0:
                b = int((n - s) / p + 1)
                if digit_sum(b, n) == s:
                    b_min = min(b_min, b)
            p += 1
    if b_min == 1L << 55:
        return -1
    else:
        return b_min


if __name__ == '__main__':
    N = int(input())
    S = int(input())
    print(main(n=N, s=S))


Fixed submission:
import math


def digit_sum(b, n):
    if b > n:
        return n
    else:
        return digit_sum(b=b, n=n // b) + n % b


def main(n, s):
    if s > n:
        return -1
    elif n == s:
        return n + 1
    else:
        b = 2
        while b * b <= n:
            if digit_sum(b, n) == s:
                return b
            b += 1

        p = 1
        b_min = -1
        while p * p <= n:
            if (n - s) % p == 0:
                b = (n - s) // p + 1
                if digit_sum(b, n) == s:
                    b_min = min(b_min, b) if b_min != -1 else b
            p += 1
        return b_min


if __name__ == '__main__':
    N = int(input())
    S = int(input())
    print(main(n=N, s=S))

Buggy python submission (verdict: Runtime Error):
import math


def digit_sum(b, n):
    if b > n:
        return n
    else:
        return digit_sum(b=b, n=n // b) + n % b


def main(n, s):
    if n == s:
        return n + 1
    elif s == 1:
        return n
    elif s > n:
        return -1
    else:
        sqrt_n = int(math.sqrt(n))
        for b in range(2, sqrt_n + 1):
            if digit_sum(b, n) == s:
                return b
        for p in range(1, sqrt_n + 1):
            b = (n - s) // (p + 1)
            if digit_sum(b, n) == s:
                return b
    return -1


if __name__ == '__main__':
    N = int(input())
    S = int(input())
    print(main(n=N, s=S))


Fixed submission:
import math


def digit_sum(b, n):
    if b > n:
        return n
    else:
        return digit_sum(b=b, n=n // b) + n % b


def main(n, s):
    if s > n:
        return -1
    elif n == s:
        return n + 1
    else:
        b = 2
        while b * b <= n:
            if digit_sum(b, n) == s:
                return b
            b += 1

        p = 1
        b_min = -1
        while p * p <= n:
            if (n - s) % p == 0:
                b = (n - s) // p + 1
                if digit_sum(b, n) == s:
                    b_min = min(b_min, b) if b_min != -1 else b
            p += 1
        return b_min


if __name__ == '__main__':
    N = int(input())
    S = int(input())
    print(main(n=N, s=S))