void initialize_node(node_type *p, const value_type &v){
p->value = p->cache = v;
p->modifier = m_traits.default_modifier();
p->priority = xorshift128();
p->size = 1;
p->children[0] = p->children[1] = nullptr;
}
void propagate(node_type *p) const {
if(p == nullptr){ return; }
const size_t k = size(p->children[0]);
const auto mod_l_cr = m_traits.split_modifier(p->modifier, k);
const auto mod_c_r = m_traits.split_modifier(mod_l_cr.second, 1);
if(p->children[0] != nullptr){
p->children[0]->modifier = m_traits.merge_modifier(
p->children[0]->modifier, mod_l_cr.first);
refresh(p->children[0]);
}
if(p->children[1] != nullptr){
p->children[1]->modifier = m_traits.merge_modifier(
p->children[1]->modifier, mod_c_r.second);
refresh(p->children[1]);
}
p->value = m_traits.resolve(1, p->value, mod_c_r.first);
p->modifier= m_traits.default_modifier();
}