Modular Inverse

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

ll extgcd(ll a, ll b, ll &x, ll &y) {
    if (!b) { x = 1; y = 0; return a; }
    ll x1, y1;
    ll g = extgcd(b, a % b, x1, y1);
    x = y1;
    y = x1 - (a / b) * y1;
    return g;
}

ll invFermat(ll a, ll mod) {
    ll res = 1, e = mod - 2;
    a %= mod;
    while (e > 0) {
        if (e & 1) res = (__int128)res * a % mod;
        a = (__int128)a * a % mod;
        e >>= 1;
    }
    return res;
}

ll invExtended(ll a, ll m) {
    ll x, y;
    ll g = extgcd(a, m, x, y);
    if (g != 1) return -1;
    return (x % m + m) % m;
}

vector<ll> invPrecompute(ll n, ll mod) {
    vector<ll> inv(n + 1);
    inv[1] = 1;
    for (ll i = 2; i <= n; i++)
        inv[i] = mod - (mod / i) % mod * inv[mod % i] % mod;
    return inv;
}