Dynamic ConvexHull Trick

struct Line
{
    mutable ll k, m, p;
    bool operator<(const Line& o) const
    {
        if (k==o.k) return m>o.m;
        return k > o.k;
    }
    bool operator<(ll x) const
    {
        return p < x;
    }
};


struct LineContainer : multiset<Line, less<>>
{
    static const ll inf = LLONG_MAX;
    ll div(ll a, ll b)
    {
        return a / b - ((a ^ b) < 0 && a % b);
    }
    bool isect(iterator x, iterator y)
    {
        if (y == end())
            return x->p = inf, 0;
        if (x->k == y->k)
            x->p = x->m < y->m ? inf : -inf;
        else
            x->p = div(y->m - x->m, x->k - y->k);
        return x->p >= y->p;
    }
    void add(ll k, ll m)
    {
        auto z = insert({k, m, 0}), y = z++, x = y;
        while (isect(y, z))
            z = erase(z);
        if (x != begin() && isect(--x, y))
            isect(x, y = erase(y));
        while ((y = x) != begin() && (--x)->p >= y->p)
            isect(x, erase(y));
    }
    ll query(ll x)
    {
        assert(!empty());
        auto l = *lower_bound(x);
        return l.k * x + l.m;
    }
};