Math Utilities

#include <bits/stdc++.h>
using namespace std;
using ll = long long;

string decimalToBase(ll n, int base) {
    if (n == 0) return "0";
    string digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
    string res;
    bool neg = n < 0;
    if (neg) n = -n;
    while (n > 0) { res += digits[n % base]; n /= base; }
    if (neg) res += '-';
    reverse(res.begin(), res.end());
    return res;
}

ll baseToDecimal(const string &s, int base) {
    ll res = 0;
    int start = 0;
    bool neg = false;
    if (s[0] == '-') { neg = true; start = 1; }
    for (int i = start; i < (int)s.size(); i++) {
        int d = isdigit(s[i]) ? s[i] - '0' : toupper(s[i]) - 'A' + 10;
        res = res * base + d;
    }
    return neg ? -res : res;
}

ll summation(ll l, ll r) {
    if (l > r) swap(l, r);
    return r * (r + 1) / 2 - (l - 1) * l / 2;
}

ll countMultiples(ll a, ll b, ll c) {
    return b / c - (a - 1) / c;
}

ll sumMultiples(ll a, ll b, ll c) {
    ll lo = (a + c - 1) / c;
    ll hi = b / c;
    if (lo > hi) return 0;
    return c * summation(lo, hi);
}

double logBase(ll a, int b) {
    return log((double)a) / log((double)b);
}