Modular Arithmetic Helpers

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

void addMod(ll& a, ll b, ll mod) { a = (a + b % mod + mod) % mod; }

void mulMod(ll& a, ll b, ll mod) { a = ((__int128)a * b) % mod; }

ll binpow(ll b, ll e, ll mod) {
  ll res = 1;
  b %= mod;
  while (e > 0) {
    if (e & 1) res = ((__int128)res * b) % mod;
    b = ((__int128)b * b) % mod;
    e >>= 1;
  }
  return res;
}

ll binpow(ll b, ll e) {
  ll res = 1;
  while (e > 0) {
    if (e & 1) res *= b;
    b *= b;
    e >>= 1;
  }
  return res;
}

ll binaryMul(ll a, ll b, ll mod) {
  ll res = 0;
  a %= mod;
  while (b > 0) {
    if (b & 1) {
      res += a;
      if (res >= mod) res -= mod;
    }
    a += a;
    if (a >= mod) a -= mod;
    b >>= 1;
  }
  return res;
}

ll bigMod(const string& s, ll mod) {
  ll res = 0;
  for (char c : s) res = (res * 10 + (c - '0')) % mod;
  return res;
}