long long mul(long long a, long long b, long long p)
{
    long long d = (long long)(a * (long double)b / p + 0.5);
    long long c = a * b - d * p;
    return c < 0 ? c + p : c;
}

请问具体的原理是什么？这样写 $a, b, p$ 大概到多少会爆？