484_temp.cpp

#include <iostream>
#include <vector>
#include <cstdint>
#include <cassert>
#include <string>

typedef int64_t Int;

std::pair<Int, Int> solveSlow(Int number, Int digit) {
    if (digit == number) {
        return {number+1, 1};
    }
    if (digit > number) {
        return {2, 0};
    }
    Int best_base = 2, best_count = 0;
    if (digit == 0) {
        best_base = number;
        best_count = 1;
    }
    for (Int base = std::max(Int(2), digit+1); base < number; ++base) {
        Int count = 0;
        for (Int temp = number; temp > 0 && temp % base == digit; temp /= base) {
            ++count;
        }
        if (best_count < count) {
            best_base = base;
            best_count = count;
        }
    }
    return {best_base, best_count};
}

std::pair<Int, Int> solve(Int number, Int digit) {
    if (digit == number) {
        return {number+1, 1};
    }
    Int best_base = 2;
    Int best_count = 0;

    if (digit == 0) {
        best_base = number;
        best_count = 1;
    }

    for (Int base = std::max(Int(2), digit+1); base < number; ++base) {
        Int sum = 1;
        Int pow = 1;
        std::vector<Int> pows{1};
        while (number - digit * sum >= 0 && (number - digit * sum) % (pow * base) == 0) {
            pow *= base;
            pows.push_back(pow);
            sum += pow;
        }
        if (pows.size() == 1u) continue;
        /*
        for (auto & it : pows) {
            std::cout << it << " ";
        }
        std::cout << std::endl;
        */
        if (best_count < (int)pows.size()-1) {
            best_base = base;
            best_count = (int)pows.size()-1;
        }
    }
    return {best_base, best_count};
}

void test() {
    for (Int number = 1; number <= 1000; ++number)
        for (Int digit = 0; digit <= 9; ++digit) {
            //std::cout << "number = " << number << "digit = " << digit << std::endl;
            if (solveSlow(number, digit) != solve(number, digit)) {
                std::cout << "number = " << number << ", digit = " << digit << std::endl;
                std::exit(0);
            }
        }
    std::exit(0);
}

int main() {
    //test();
    Int number, digit;
    std::cin >> number >> digit;
    //assert(number <= 100);
    //assert((number == 49 && digit == 1) || (number == 7 && digit == 5));
    auto answ = solve(number, digit);
    std::cout << answ.first << " " << answ.second << std::endl;
    return 0;
}