#include <vector>
#include <utility>
#include <algorithm>
#include <cassert>
#include <string>



#include <iostream>


template<
    class TopTreeVertexData,
    class TopTreeClusterData,
    class TopTreeClusterEffect
>
struct TopTree{
public:
    struct TopTreeNode;
    struct UnderlyingTreeVertex;
private:
    void soft_expose(UnderlyingTreeVertex* l, UnderlyingTreeVertex* r){
        r->exposing_target();
        auto n_l = l->handle;
        auto n_r = r->handle;
        if(n_l == n_r){
            if(n_r->boundary_left == r || n_r->boundary_right == l){
                n_r->reverse_boundary_vertices();
                n_r->lazy_propagation();
            }
        }
        else{
            l->exposing_source(r);
            n_r = r->handle;
            if(n_r->right_child == n_l) n_r->reverse_boundary_vertices();
            n_r->lazy_propagation();
            n_l->lazy_propagation();
        }
    }
    void undo_hard_expose(){
        for(int i=hard_expose_new_rakes_length-1; i>=0; i--){
            hard_expose_new_rakes[i].first->lazy_propagation();
        }
        for(int i=hard_expose_new_rakes_length-1; i>=0; i--){
            if(hard_expose_new_rakes[i].second) delete(hard_expose_new_rakes[i].first);
        }
        hard_expose_new_rakes_length = 0;

        for(int i=0; i<hard_expose_undo_length; i++){
            hard_expose_undo_memo[i].execute();
        }
        hard_expose_undo_length = 0;
    }
public:

    struct TopTreeNode{
    public:

        TopTreeNode* parent = nullptr;
        TopTreeNode* right_child = nullptr;
        TopTreeNode* left_child = nullptr;
        TopTreeNode* mid_child = nullptr;
        UnderlyingTreeVertex* boundary_left = nullptr;
        UnderlyingTreeVertex* boundary_right = nullptr;
        bool bouundary_vertices_are_reversed = false;
        enum TopTreeNodeType { NODE_TYPE_DISABLED, NODE_TYPE_EDGE, NODE_TYPE_RAKE, NODE_TYPE_COMPRESS };
        TopTreeNodeType node_type = NODE_TYPE_DISABLED;

        TopTreeClusterData data = TopTreeClusterData::init();
        TopTreeClusterEffect lazy_data = TopTreeClusterEffect::id();

        void get_propagated(){
            TopTreeNode* pp = parent;
            TopTreeNode* p = this;
            TopTreeNode* tmp = nullptr;
            p->parent = nullptr;
            while(pp){
                tmp = pp->parent;
                pp->parent = p;
                p = pp;
                pp = tmp;
            }
            while(p){
                p->lazy_propagation();
                tmp = p->parent;
                p->parent = pp;
                pp = p;
                p = tmp;
            }
        }

    private:
        void disable(){
            node_type = NODE_TYPE_DISABLED;
            parent = nullptr;
            left_child = nullptr;
            right_child = nullptr;
            mid_child = nullptr;
            boundary_left = nullptr;
            boundary_right = nullptr;
            bouundary_vertices_are_reversed = false;
        }
        TopTreeNode*& parentchild(){
            TopTreeNode* p = parent;
            if(p->left_child == this) return p->left_child;
            if(p->right_child == this) return p->right_child;
            if(p->mid_child == this) return p->mid_child;
            exit(1);
        }

    public:

        void block(){
            if(left_child) left_child->parent = nullptr;
            if(right_child) right_child->parent = nullptr;
            if(mid_child) mid_child->parent = nullptr;
        }
        void unblock(TopTreeNode* new_root){
            if (left_child && !left_child->is_root()) left_child = new_root;
            if (right_child && !right_child->is_root()) right_child = new_root;
            if (mid_child && !mid_child->is_root()) mid_child = new_root;
            if(node_type == NODE_TYPE_COMPRESS){
                bottomup_compress(left_child, mid_child, right_child);
            }
            if(node_type == NODE_TYPE_RAKE){
                bottomup_rake(left_child, right_child);
            }
        }

        void reverse_boundary_vertices(){
            bouundary_vertices_are_reversed = !bouundary_vertices_are_reversed;
            std::swap(boundary_left, boundary_right);
            data.reverse();
            if(node_type == NODE_TYPE_COMPRESS){
                std::swap(left_child, right_child);
            }
        }
        
        void apply_lazy_data(TopTreeClusterEffect f){
            lazy_data = TopTreeClusterEffect::composition(f, lazy_data);
            data = TopTreeClusterEffect::mapping_cluster(f, data);
        }
        void lazy_propagation(){
            if(bouundary_vertices_are_reversed){
                if(node_type == NODE_TYPE_COMPRESS){
                    left_child->reverse_boundary_vertices();
                    right_child->reverse_boundary_vertices();
                }
            }
            bouundary_vertices_are_reversed = false;

            auto f = lazy_data;
            if(node_type == NODE_TYPE_COMPRESS){
                left_child->apply_lazy_data(f);
                if(mid_child){
                    mid_child->apply_lazy_data(f);
                    mid_child->boundary_left->data = TopTreeClusterEffect::mapping_vertex(f, mid_child->boundary_left->data);
                }
                right_child->apply_lazy_data(f);
                left_child->boundary_right->data = TopTreeClusterEffect::mapping_vertex(f, left_child->boundary_right->data);
            }
            if(node_type == NODE_TYPE_RAKE){
                left_child->apply_lazy_data(f);
                right_child->apply_lazy_data(f);
                right_child->boundary_left->data = TopTreeClusterEffect::mapping_vertex(f, right_child->boundary_left->data);
            }
            lazy_data = TopTreeClusterEffect::id();
        }

        void bottomup_edge(UnderlyingTreeVertex* l, UnderlyingTreeVertex* r, TopTreeClusterData x){
            node_type = NODE_TYPE_EDGE;
            left_child = nullptr;
            right_child = nullptr;
            mid_child = nullptr;
            boundary_left = l;
            boundary_right = r;
            l->handle = this;
            r->handle = this;
            data = x;
            lazy_data = TopTreeClusterEffect::id();
        }
        void bottomup_rake(TopTreeNode* l, TopTreeNode* r, bool special_for_hard_expose = false){
            if(l->node_type != NODE_TYPE_RAKE) l->boundary_left->handle = l;
            if(r->node_type != NODE_TYPE_RAKE) r->boundary_left->handle = r;
            if (!special_for_hard_expose) {
                node_type = NODE_TYPE_RAKE;
                boundary_left = l->boundary_left;
                boundary_right = l->boundary_right;
                left_child = l;
                l->parent = this;
                mid_child = nullptr;
                right_child = r;
                r->parent = this;
                data = TopTreeClusterData::rake(left_child->data, right_child->data, right_child->boundary_left->data);
            }
            else {
                node_type = NODE_TYPE_RAKE;
                boundary_left = l->boundary_left;
                boundary_right = l->boundary_right;
                left_child = l;
                l->parent = this;
                mid_child = nullptr;
                right_child = r;
                r->parent = this;
                auto buf = left_child->data;
                buf.reverse();
                buf = TopTreeClusterData::rake(buf, right_child->data, right_child->boundary_left->data);
                buf.reverse();
                data = buf;
            }
        }
        void bottomup_compress(TopTreeNode* l, TopTreeNode* m_rake, TopTreeNode* r){
            assert(l->boundary_right == r->boundary_left);
            UnderlyingTreeVertex* bound = l->boundary_right;
            node_type = NODE_TYPE_COMPRESS;
            boundary_left = l->boundary_left;
            boundary_right = r->boundary_right;
            left_child = l;
            l->parent = this;
            mid_child = m_rake;
            if(m_rake) m_rake->parent = this;
            right_child = r;
            r->parent = this;

            if(mid_child && mid_child->node_type != NODE_TYPE_RAKE) mid_child->boundary_left->handle = mid_child;

            boundary_left->handle = this;
            bound->handle = this;
            boundary_right->handle = this;
            auto cent = left_child->boundary_right;
            auto l_data = left_child->data;
            if (mid_child) l_data = TopTreeClusterData::rake(l_data, mid_child->data, mid_child->boundary_left->data);
            data = TopTreeClusterData::compress(l_data, cent->data, right_child->data);
        }

        void rotate_rake_left(){
            auto p = parent;
            
            if(!p->is_root()) p->parentchild() = this;
            parent = p->parent;

            auto c1 = left_child;
            p->bottomup_rake(p->left_child, c1);
            bottomup_rake(p, right_child);
        }
        void rotate_rake_right(){
            auto p = parent;
            
            if(!p->is_root()) p->parentchild() = this;
            parent = p->parent;

            auto c1 = right_child;
            p->bottomup_rake(c1, p->right_child);
            bottomup_rake(left_child, p);
        }
        void rotate_compress_left(){
            auto p = parent;
            
            if(!p->is_root()) p->parentchild() = this;
            parent = p->parent;

            auto c4 = this->left_child;
            p->bottomup_compress(p->left_child, p->mid_child, c4);
            bottomup_compress(p, mid_child, right_child);
        }
        void rotate_compress_right(){
            auto p = parent;
            
            if(!p->is_root()) p->parentchild() = this;
            parent = p->parent;

            auto c3 = this->right_child;
            p->bottomup_compress(c3, p->mid_child, p->right_child);
            bottomup_compress(left_child, mid_child, p);
        }

        
        void splay_soft_rake(){
            while(!is_rake_root()){
                auto p = parent;
                if(p->is_rake_root()){
                    if(p->left_child == this){ rotate_rake_right(); }
                    else{ rotate_rake_left(); }
                }
                else{
                    auto pp = p->parent;
                    if(p->left_child == this){
                        if(pp->left_child == p){ p->rotate_rake_right(); rotate_rake_right(); }
                        else { rotate_rake_right(); rotate_rake_left(); }
                    }
                    else{
                        if(pp->right_child == p){ p->rotate_rake_left(); rotate_rake_left(); }
                        else { rotate_rake_left(); rotate_rake_right(); }
                    }
                }
            }
        }
        void splay_rake(){
            if(is_rake_root()) return;
            auto p1 = parent;
            p1->splay_soft_rake();
            auto p2 = parent;
            if(p2 == p1) return;
            p2->splay_soft_rake();
        }
        void splay_compress(){
            while(!is_compress_root()){
                auto p = parent;
                if(p->is_compress_root()){
                    if(p->left_child == this){ rotate_compress_right(); }
                    else{ rotate_compress_left(); }
                }
                else{
                    auto pp = p->parent;
                    if(p->left_child == this){
                        if(pp->left_child == p){ p->rotate_compress_right(); rotate_compress_right(); }
                        else { rotate_compress_right(); rotate_compress_left(); }
                    }
                    else{
                        if(pp->right_child == p){ p->rotate_compress_left(); rotate_compress_left(); }
                        else { rotate_compress_left(); rotate_compress_right(); }
                    }
                }
            }
        }
        void splice(bool compress_on_left = true){
            TopTreeNode* p = nullptr;

            TopTreeNode* rake_l = nullptr;
            TopTreeNode* rake_lp = nullptr;
            TopTreeNode* rake_r = nullptr;
            TopTreeNode* rake_rp = nullptr;
            p = parent;
            bool is_this_left_child = (p->left_child == this);
            while(p->node_type == NODE_TYPE_RAKE){
                if(is_this_left_child){
                    rake_r = p->right_child;
                    rake_rp = p;
                }
                else{
                    rake_l = p->left_child;
                    rake_lp = p;
                }
                auto pp = p->parent;
                is_this_left_child = (pp->left_child == p);
                p = pp;
            }

            if(compress_on_left){
                auto rake_r1 = p->left_child;
                if(rake_l){ rake_lp->bottomup_rake(rake_l, rake_r1); rake_r1 = rake_lp; }
                if(rake_r){ rake_rp->bottomup_rake(rake_r1, rake_r); rake_r1 = rake_rp; }
                p->bottomup_compress(this, rake_r1, p->right_child);
            }
            else{
                reverse_boundary_vertices();
                auto rake_r1 = p->right_child;
                rake_r1->reverse_boundary_vertices();
                if(rake_l){ rake_lp->bottomup_rake(rake_l, rake_r1); rake_r1 = rake_lp; }
                if(rake_r){ rake_rp->bottomup_rake(rake_r1, rake_r); rake_r1 = rake_rp; }
                p->bottomup_compress(p->left_child, rake_r1, this);
            }
        }



        bool is_enabled() const { return node_type != NODE_TYPE_DISABLED; }
        bool is_rake_root() const { return !parent || parent->node_type != NODE_TYPE_RAKE; }
        bool is_compress_root() const {
            if(!parent) return true;
            if(parent->node_type != NODE_TYPE_COMPRESS) return true;
            return parent->mid_child == this;
        }
        bool is_root() const { return !parent; }

    };

    struct UnderlyingTreeVertex{
        TopTreeNode* handle;
        TopTreeVertexData data;

        UnderlyingTreeVertex(){
            handle = nullptr;
            data = TopTreeVertexData::init();
        }
        void exposing_target(){
            TopTreeNode* n_this = handle;
            
            handle->get_propagated();

            auto c = n_this;
            while(!c->is_root()){
                if(!c->is_compress_root()){
                    c->splay_compress();
                    continue;
                }
                if(!c->is_rake_root()){
                    c->splay_rake();
                    while(!c->is_rake_root()) c = c->parent;
                    continue;
                }
                c = c->parent;
            }

            c = n_this = handle;
            while(!c->is_root()){
                c->splice();
                c = c->parent;
            }

            handle->get_propagated();
            handle->splay_compress();
        }
        bool exposing_source(UnderlyingTreeVertex* target){
            auto n_this = handle;
            auto n_target = target->handle;
            
            if(n_this == n_target) return true;
            if(n_target->node_type == TopTreeNode::NODE_TYPE_EDGE) return false;
            if(n_this->is_root()) return false;
            if(n_target->boundary_left == target) n_target->reverse_boundary_vertices();
            if(n_target->boundary_right == target){
                exposing_target();
                return true;
            }
            
            handle->get_propagated();

            // block
            n_target->left_child->parent = nullptr;
            n_target->right_child->parent = nullptr;

            auto c = n_this;
            while(!c->is_root()){
                if(!c->is_compress_root()){
                    c->splay_compress();
                    continue;
                }
                if(!c->is_rake_root()){
                    c->splay_rake();
                    while(!c->is_rake_root()) c = c->parent;
                    continue;
                }
                c = c->parent;
            }

            if (!n_target->left_child->is_root()) n_target->left_child = c;
            if (!n_target->right_child->is_root()) n_target->right_child = c;

            c = n_this = handle;
            while(!c->is_root()){
                auto p = c;
                while(!p->is_rake_root()) p = p->parent;
                
                bool compress_to_left = true;
                if(n_target->right_child == p->parent) compress_to_left = false;
                c->splice(compress_to_left);
                c = c->parent;
                if(n_target == c){
                    n_target->left_child->parent = nullptr;
                    n_target->right_child->parent = nullptr;
                }
            }

            c = handle;
            c->get_propagated();
            c->splay_compress();
            if (!n_target->left_child->is_root()) n_target->left_child = c;
            if (!n_target->right_child->is_root()) n_target->right_child = c;
            n_target->bottomup_compress(n_target->left_child, n_target->mid_child, n_target->right_child);
            if(c->is_root()) return false;

            if(n_target->right_child == c){
                n_target->reverse_boundary_vertices();
                n_target->lazy_propagation();
            }
            return true;
        }
    };

    TopTreeNode* expose(UnderlyingTreeVertex* l){
        undo_hard_expose();

        if(!l->handle) return nullptr;

        UnderlyingTreeVertex* r = nullptr;
        if(l->handle->boundary_left != l) r = l->handle->boundary_left;
        if(l->handle->boundary_right != l) r = l->handle->boundary_right;

        return expose(l, r);
    }
    TopTreeNode* expose(UnderlyingTreeVertex* l, UnderlyingTreeVertex* r, bool do_hard = true){
        undo_hard_expose();

        // soft expose
        soft_expose(l, r);
        auto n_l = l->handle;
        auto n_r = r->handle;

        // hard expose
        if(do_hard){
            auto hard_expose_rake_case1 = [this](TopTreeNode* c)->void {
                hard_expose_undo_memo[hard_expose_undo_length++] = HardExposeUndoUnit(c);
                hard_expose_undo_memo[hard_expose_undo_length - 1].r_reversed = true;
                c->right_child->reverse_boundary_vertices();
                TopTreeNode* rake_r = c->right_child;
                if(c->mid_child){
                    auto tmp = new TopTreeNode();
                    tmp->bottomup_rake(c->mid_child, rake_r);
                    rake_r = tmp;
                    hard_expose_new_rakes[hard_expose_new_rakes_length++] = std::make_pair(rake_r, true);
                }
                c->bottomup_rake(c->left_child, rake_r, false);
                hard_expose_new_rakes[hard_expose_new_rakes_length++] = std::make_pair(c, false);
            };
            auto hard_expose_rake_case2 = [this](TopTreeNode* c)->void {
                hard_expose_undo_memo[hard_expose_undo_length++] = HardExposeUndoUnit(c);
                TopTreeNode* rake_r = c->left_child;
                if(c->mid_child){
                    auto tmp = new TopTreeNode();
                    tmp->bottomup_rake(rake_r, c->mid_child);
                    rake_r = tmp;
                    hard_expose_new_rakes[hard_expose_new_rakes_length++] = std::make_pair(rake_r, true);
                }
                c->bottomup_rake(c->right_child, rake_r, true);
                hard_expose_new_rakes[hard_expose_new_rakes_length++] = std::make_pair(c, false);
            };

            n_r->lazy_propagation();
            n_l->lazy_propagation();

            if(n_r->boundary_left == l && n_r->boundary_right == r){ /* case (3) (4) do nothing */ }
            else if(n_r->boundary_left == l){ /* case (1) */ hard_expose_rake_case1(n_r); }
            else if(n_r->boundary_right == r){ /* case (2) */ hard_expose_rake_case2(n_r); }
            else{ /* case (5) */ hard_expose_rake_case2(n_l); hard_expose_rake_case1(n_r); }
        }

        return n_r;
    }
    bool cut(UnderlyingTreeVertex* l, UnderlyingTreeVertex* r, TopTreeClusterData* data_out){
        undo_hard_expose();

        auto fix_tmporary_state = [this](TopTreeNode* c)->TopTreeNode*{
            if(c->mid_child){
                if(c->mid_child->node_type == TopTreeNode::NODE_TYPE_RAKE){
                    // case (3)
                    auto most_left_rake = c->mid_child;
                    most_left_rake->lazy_propagation();
                    while(most_left_rake->left_child->node_type == TopTreeNode::NODE_TYPE_RAKE){
                        most_left_rake = most_left_rake->left_child;
                        most_left_rake->lazy_propagation();
                    }
                    most_left_rake->splay_soft_rake();
                    most_left_rake = most_left_rake->left_child;
                    most_left_rake->reverse_boundary_vertices();
                    c->bottomup_compress(c->left_child, c->mid_child->right_child, most_left_rake);
                }
                else{
                    // case (2)
                    c->mid_child->reverse_boundary_vertices();
                    c->bottomup_compress(c->left_child, nullptr, c->mid_child);
                }
            }
            else{
                // case (1)
                auto cc = c->left_child;
                cc->parent = nullptr;
                delete(c);
                c = cc;
                c->boundary_left->handle = c;
                c->boundary_right->handle = c;
            }
            return c;
        };

        soft_expose(l, r);
        auto n_l = l->handle;
        auto n_r = r->handle;

        if(n_r->node_type == TopTreeNode::NODE_TYPE_EDGE){
            // case (4)
            l->handle = r->handle = nullptr;
            if(data_out) *data_out = n_l->data;
            delete(n_l);
            return true;
        }
        if(n_r->boundary_left == l && n_r->boundary_right == r){
            // case (3)
            return false;
        }
        if(n_r->boundary_left == l){
            // case (1)
            n_r->reverse_boundary_vertices();
            std::swap(l, r);
            // reduce to case (2)
        }
        if(n_r->boundary_right == r){
            // case (2)
            n_r->lazy_propagation();
            auto lr = n_r->right_child;
            if(lr->node_type != TopTreeNode::NODE_TYPE_EDGE) return false;
            if(data_out) *data_out = lr->data;
            delete(lr);
            n_r->right_child = nullptr;
            fix_tmporary_state(n_r);
            r->handle = nullptr;
            return true;
        }
        // case (5)
        n_r->lazy_propagation();
        n_l->lazy_propagation();
        auto lr = n_l->right_child;
        if(lr->node_type != TopTreeNode::NODE_TYPE_EDGE) return false;
        if(data_out) *data_out = lr->data;
        delete(lr);
        n_r->left_child = nullptr;
        n_l->right_child = nullptr;
        n_l->parent = nullptr;
        fix_tmporary_state(n_l);
        n_r->left_child = n_r->right_child;
        n_r->left_child->reverse_boundary_vertices();
        fix_tmporary_state(n_r);
        return true;
    }
    bool link(UnderlyingTreeVertex* l, UnderlyingTreeVertex* r, TopTreeClusterData x){
            undo_hard_expose();

            auto make_temporary_state = [this](UnderlyingTreeVertex* c)->TopTreeNode* {
                auto n_c = c->handle;
                if(n_c->boundary_left == c){
                    n_c->reverse_boundary_vertices();
                }
                if(n_c->boundary_right == c){
                    // c is a leaf
                    auto unstable_root = new TopTreeNode();
                    n_c->parent = unstable_root;
                    unstable_root->left_child = n_c;
                    return unstable_root;
                }
                // c is not a leaf
                n_c->lazy_propagation();
                auto r_rake = n_c->right_child;
                n_c->right_child = nullptr;
                r_rake->reverse_boundary_vertices();
                if(n_c->mid_child){
                    auto rake_root = new TopTreeNode();
                    rake_root->bottomup_rake(n_c->mid_child, r_rake);
                    r_rake = rake_root;
                }
                n_c->mid_child = r_rake;
                r_rake->parent = n_c;
                n_c->node_type = TopTreeNode::NODE_TYPE_DISABLED;
                return n_c;
            };

            if(!l->handle) std::swap(l, r);
            if(!l->handle){
                // cut case (4)
                TopTreeNode* c = new TopTreeNode();
                c->bottomup_edge(l, r, x);
                return true;
            }
            if(!r->handle){
                // r->handle == nullptr : cut case (2)
                l->exposing_target();
                auto n_l = make_temporary_state(l);
                auto lr = new TopTreeNode();
                lr->bottomup_edge(l, r, x);
                n_l->bottomup_compress(n_l->left_child, n_l->mid_child, lr);
                return true;
            }
            // cut case (5)
            l->exposing_target();
            r->exposing_target();
            if(l->handle == r->handle) return false;
            if(!l->handle->is_root()) return false;
            auto n_l = make_temporary_state(l);
            auto n_r = make_temporary_state(r);
            std::swap(n_r->left_child, n_r->right_child);
            n_r->right_child->reverse_boundary_vertices();
            auto lr = new TopTreeNode();
            lr->bottomup_edge(l, r, x);
            n_r->bottomup_compress(lr, n_r->mid_child, n_r->right_child);
            n_l->bottomup_compress(n_l->left_child, n_l->mid_child, n_r);
            return true;
        }


    struct HardExposeUndoUnit{
        TopTreeNode* to = nullptr;
        TopTreeNode* l = nullptr;
        bool l_reversed = false;
        TopTreeNode* m_rake = nullptr;
        bool m_rake_reversed = false;
        TopTreeNode* r = nullptr;
        bool r_reversed = false;
        HardExposeUndoUnit(){}
        HardExposeUndoUnit(TopTreeNode* v){
            to = v;
            l = v->left_child;
            m_rake = v->mid_child;
            r = v->right_child;
        }
        void execute(){
            if (l_reversed) l->reverse_boundary_vertices();
            if (m_rake_reversed) m_rake->reverse_boundary_vertices();
            if (r_reversed) r->reverse_boundary_vertices();
            to->bottomup_compress(l, m_rake, r);
        }
    };

    int hard_expose_undo_length = 0;
    HardExposeUndoUnit hard_expose_undo_memo[2];
    int hard_expose_new_rakes_length = 0;
    std::pair<TopTreeNode*, bool> hard_expose_new_rakes[10] = {};
};



#include <vector>
#include <algorithm>
#include <iostream>

namespace nachia {

    struct LinkCutTree {
        struct S { long long x; };
        static S op(S l, S r) { return { l.x + r.x }; }
        static S e() { return { 0 }; }
        static void reverseprod(S& x) {}
        struct F {  };
        static S mapping(F f, S x) { return x; }
        static F composition(F f, F x) { return x; }
        static F id() { return {}; }


        struct Node {
            Node* l = 0, * r = 0, * p = 0;
            S a = e();
            S prod = e();
            F f = id();
            // lazy & 1 : reverse
            // lazy & 2 : deta
            int lazy = 0;
            
            void prepareDown() {
                if(lazy & 2){
                    if(l) {
                        l->a = mapping(f, l->a);
                        l->prod = mapping(f, l->prod);
                        l->f = composition(f, l->f);
                        l->lazy |= 2;
                    }
                    if(r) {
                        r->a = mapping(f, r->a);
                        r->prod = mapping(f, r->prod);
                        r->f = composition(f, r->f);
                        r->lazy |= 2;
                    }
                    f = id();
                }
                if (lazy & 1) {
                    ::std::swap(l, r);
                    if (l) { l->lazy ^= 1; reverseprod(l->prod); }
                    if (r) { r->lazy ^= 1; reverseprod(r->prod); }
                }
                lazy = 0;
            }
            void prepareUp() {
                auto res = a;
                if(l) res = op(l->prod, res);
                if(r) res = op(res, r->prod);
                prod = res;
            }
            Node** p_parentchild() {
                if(!p) return nullptr;
                if(p->l == this) return &p->l;
                else if(p->r == this) return &p->r;
                return nullptr;
            }
            void rotL() {
                Node* t = p;
                Node** parentchild_p = t->p_parentchild();
                if(parentchild_p){ *parentchild_p = this; }
                p = t->p;
                t->p = this;
                t->r = l;
                if(l) l->p = t;
                l = t;
            }
            void rotR() {
                Node* t = p;
                Node** parentchild_p = t->p_parentchild();
                if(parentchild_p){ *parentchild_p = this; }
                p = t->p;
                t->p = this;
                t->l = r;
                if(r) r->p = t;
                r = t;
            }
        };

        ::std::vector<Node> A;
        LinkCutTree(int n = 0) {
            A.resize(n);
        }
        LinkCutTree(const ::std::vector<S>& a) : LinkCutTree(a.size()) {
            for (int i = 0; i < (int)a.size(); i++) A[i].prod = A[i].a = a[i];
        }
        Node* at(int idx) {
            return &A[idx];
        }
        void splay(Node* c) {
            c->prepareDown();
            while(true) {
                Node* p = c->p;
                if(!p) break;
                Node* pp = p->p;
                if(pp) pp->prepareDown();
                p->prepareDown();
                c->prepareDown();
                if(p->l == c){
                    if(!pp){ c->rotR(); }
                    else if(pp->l == p){ p->rotR(); c->rotR(); }
                    else if(pp->r == p){ c->rotR(); c->rotL(); }
                    else{ c->rotR(); }
                }
                else if(p->r == c){
                    if(!pp){ c->rotL(); }
                    else if(pp->r == p){ p->rotL(); c->rotL(); }
                    else if(pp->l == p){ c->rotL(); c->rotR(); }
                    else{ c->rotL(); }
                }
                else break;
                if(pp) pp->prepareUp();
                p->prepareUp();
            }
            c->prepareUp();
        }
        void expose(Node* c) {
            auto p = c;
            while(p){ splay(p); p = p->p; }
            p = c;
            while(p->p){ p->p->r = p; p = p->p; }
            splay(c);
            c->r = nullptr;
            c->prod = (c->l ? op(c->l->prod, c->a) : c->a);
        }
        void evert(Node* c) {
            expose(c);
            c->lazy ^= 1;
            reverseprod(c->prod);
            c->prepareDown();
        }
        void link(Node* c, Node* r) {
            if(c == r) return;
            evert(c);
            evert(r);
            if(c->p) return;
            c->p = r;
        }
        void cut(Node* c) {
            expose(c);
            if(!c->l) return;
            c->l->p = nullptr;
            c->l = nullptr;
        }
        // [u,v)
        // post : evert(u) , splayLC(v)
        Node* between(Node* u, Node* v) {
            if(u == v) return nullptr;
            evert(u);
            expose(v);
            v->l->prepareDown();
            return v->l;
        }
        S prod(Node* s, Node* t) {
            auto resv = between(s, t);
            if(!resv) return t->a;
            S res = resv->prod;
            res = op(res, t->a);
            return res;
        }
        S get(Node* p) {
            expose(p);
            return p->a;
        }
        void set(Node* p, S x) {
            expose(p);
            p->a = x;
            p->prepareUp();
        }
    };

}

#include <vector>
#include <algorithm>

namespace nachia {

struct Dsu{
private:
    int N;
    std::vector<int> P;
    std::vector<int> H;
public:
    Dsu() : N(0) {}
    Dsu(int n) : N(n), P(n, -1), H(n) {
        for(int i=0; i<n; i++) H[i] = i;
    }
    int leader(int u){
        if(P[u] < 0) return u;
        int v = P[u];
        while(P[v] >= 0){ P[u] = P[v]; u = v; v = P[v]; }
        return P[u];
    }
    int append(){
        int n = P.size();
        P.push_back(-1);
        H.push_back(n);
        return n;
    }
    int label(int u){ return H[leader(u)]; }
    int operator[](int u){ return H[leader(u)]; }
    void merge(int u, int v, int newLabel){
        if(newLabel < 0) newLabel = u;
        u = leader(u);
        v = leader(v);
        if(u == v){ H[u] = newLabel; return; }
        N--;
        if(-P[u] < -P[v]) std::swap(u, v);
        P[u] += P[v];
        H[P[v] = u] = newLabel;
    }
    int merge(int u, int v){ merge(u, v, u); return u; }
    int count(){ return N; }
    int size(int u){ return -P[leader(u)]; }
    bool same(int u, int v){ return leader(u) == leader(v); }
};

} // namespace nachia


struct TopTreeVertexData{
    static TopTreeVertexData init(){ return {}; }
};
struct TopTreeClusterData{
    long long l, r, len, diam;
    static TopTreeClusterData edge(long long w){
        return { w, w, w, w };
    }
    static TopTreeClusterData init(){ return { 0,0,0,0 }; }
    static TopTreeClusterData compress(TopTreeClusterData l, TopTreeVertexData, TopTreeClusterData r){
        return {
            std::max(l.l, l.len + r.l),
            std::max(r.r, r.len + l.r),
            l.len + r.len,
            std::max(std::max(l.diam, r.diam), l.r + r.l)
        };
    }
    static TopTreeClusterData rake(TopTreeClusterData l, TopTreeClusterData r, TopTreeVertexData){
        return {
            std::max(l.l, l.len + r.r),
            std::max(l.r, r.r),
            l.len,
            std::max(std::max(l.diam, r.diam), l.r + r.r)
        };
    }
    void reverse(){
        std::swap(l, r);
    }
};
struct TopTreeClusterEffect{
    static TopTreeClusterEffect id(){ return {  }; }
    static TopTreeClusterData mapping_cluster(TopTreeClusterEffect, TopTreeClusterData x){
        return x;
    }
    static TopTreeVertexData mapping_vertex(TopTreeClusterEffect, TopTreeVertexData x){
        return x;
    }
    static TopTreeClusterEffect composition(TopTreeClusterEffect l, TopTreeClusterEffect){
        return { l };
    }
    void reverse(){}
};

#include <iostream>
using namespace std;
#define rep(i,n) for(int i=0; i<(int)(n); i++)

int main(){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    long long N, X, Q; cin >> N >> X >> Q;
    auto tree = nachia::LinkCutTree(N*2-1);
    using TopTreeInst = TopTree<TopTreeVertexData, TopTreeClusterData, TopTreeClusterEffect>;
    TopTreeInst toptree;
    vector<TopTreeInst::UnderlyingTreeVertex> vtxs(N);
    auto dsu = nachia::Dsu(N);
    long long ecnt = N;
    rep(i,Q){
        int t; cin >> t;
        if(t == 1){
            int v, w; cin >> v >> w;
            tree.set(tree.at(ecnt), {w});
            tree.link(tree.at(v), tree.at(ecnt));
            tree.link(tree.at(X), tree.at(ecnt));
            toptree.link(&vtxs[X], &vtxs[v], TopTreeClusterData::edge(w));
            dsu.merge(v, X);
            ecnt++;
        }
        if(t == 2){
            int u, v; cin >> u >> v;
            if(!dsu.same(u, v)){
                cout << "-1\n";
            }
            else{
                long long x = tree.prod(tree.at(u), tree.at(v)).x;
                X = (X + x) % N;
                cout << x << '\n';
            }
        }
        if(t == 3){
            int v; cin >> v;
            if(dsu.size(v) == 1){
                cout << "0\n";
            }
            else{
                auto c = toptree.expose(&vtxs[v]);
                cout << c->data.diam << '\n';
            }
        }
        if(t == 4){
            long long v; cin >> v;
            X = (X + v) % N;
        }
    }
}