https://uva.onlinejudge.org/external/100/10093.pdf

uva10093_esay_problem.cpp

#include <iostream>
#include <string>

using namespace std;

int to_decimal(char c)
{
    if (isdigit(c))
    {
        return c - '0';
    }
    else if (isupper(c))
    {
        return c - 'A' + to_decimal('9') + 1;
    }
    else if (islower(c))
    {
        return c - 'a' + to_decimal('Z') + 1;
    }

    return 0;
}

bool verify(int base, const string& r)
{
    if (r.empty()) return true;

    bool is_signed = r.front() == '+' || r.front() == '-';

    auto remainder = 0;
    for (size_t i = is_signed ? 1 : 0; i < r.size(); i++)
    {
        auto num = to_decimal(r[i]);
        if (num >= base) return false;

        remainder = (remainder + num) % (base - 1);
    }
    return remainder == 0;
}

void test_case(const string& r)
{
    for (int base = 2; base <= 62; base++)
    {
        if (verify(base, r))
        {
            cout << base << endl;
            return;
        }
    }
    cout << "such number is impossible!" << endl;
}

int main()
{
    string r;
    while (cin >> r) test_case(r);
    return 0;
}