逆元

逆元

1.

void exgcd (LL a, LL b, LL &x, LL &y) {
    if (b == 0) {
        x = 1; y = 0;
        return;
    }
    exgcd (b, a % b, y, x);
    y -= a / b * x;
}

LL inv (LL a, LL p) {
	LL x, y;
	exgcd (a, p, x, y);
//	printf ("a = %d, p = %d, x = %d, y = %d\n", a, p, x, y);
	LL tox = lcm (a, p) / a, toy = lcm (a, p) / p;
	LL need = x / tox;
	x += need * tox; y -= need * toy;
	if (x < 0) x += tox, y -= toy;
//	printf ("a = %d, p = %d, x = %d, y = %d, tox = %d, toy = %d\n\n", a, p, x, y, tox, toy);
	return x;
}

LL gcd (LL x, LL y) {
	if (y == 0) return x;
	else return gcd (y, x % y);
}

LL lcm (LL x, LL y) {
	return x / gcd (x, y) * y;
}

2.

LL quick_pow (LL a, LL b, LL p) {
	LL ans = 1;
	while (b) {
		if (b & 1) ans = (ans * a) % p;
		a = (a * a) % p;
		b >>= 1;
	}
	return ans;
}

LL inv (LL a, LL p) {
//	printf ("a = %d, p = %d\n", a, p);
	return quick_pow (a, p - 2, p);
}