#include <bits/stdc++.h>
#pragma GCC diagnostic ignored "-Wsign-compare"
#pragma GCC diagnostic ignored "-Wsign-conversion"

using i32 = int32_t;
using i64 = int64_t;
using u32 = uint32_t;
using u64 = uint64_t;
using uint = unsigned int;
using usize = std::size_t;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
template<typename T> constexpr T popcount(const T u) { return u ? static_cast<T>(__builtin_popcountll(static_cast<u64>(u))) : static_cast<T>(0); }
template<typename T> constexpr T log2p1(const T u) { return u ? static_cast<T>(64 - __builtin_clzll(static_cast<u64>(u))) : static_cast<T>(0); }
template<typename T> constexpr T msbp1(const T u) { return log2p1(u); }
template<typename T> constexpr T lsbp1(const T u) { return __builtin_ffsll(u); }
template<typename T> constexpr T clog(const T u) { return u ? log2p1(u - 1) : static_cast<T>(u); }
template<typename T> constexpr bool ispow2(const T u) { return u and (static_cast<u64>(u) & static_cast<u64>(u - 1)) == 0; }
template<typename T> constexpr T ceil2(const T u) { return static_cast<T>(1) << clog(u); }
template<typename T> constexpr T floor2(const T u) { return u == 0 ? static_cast<T>(0) : static_cast<T>(1) << (log2p1(u) - 1); }
template<typename T> constexpr bool btest(const T mask, const usize ind) { return static_cast<bool>((static_cast<u64>(mask) >> ind) & static_cast<u64>(1)); }
template<typename T> void bset(T& mask, const usize ind) { mask |= (static_cast<T>(1) << ind); }
template<typename T> void breset(T& mask, const usize ind) { mask &= ~(static_cast<T>(1) << ind); }
template<typename T> void bflip(T& mask, const usize ind) { mask ^= (static_cast<T>(1) << ind); }
template<typename T> void bset(T& mask, const usize ind, const bool b) { (b ? bset(mask, ind) : breset(mask, ind)); }
template<typename T> constexpr T bcut(const T mask, const usize ind) { return ind == 0 ? static_cast<T>(0) : static_cast<T>((static_cast<u64>(mask) << (64 - ind)) >> (64 - ind)); }
template<typename T> bool chmin(T& a, const T& b) { return (a > b ? a = b, true : false); }
template<typename T> bool chmax(T& a, const T& b) { return (a < b ? a = b, true : false); }
constexpr unsigned int mod                  = 1000000007;
template<typename T> constexpr T inf_v      = std::numeric_limits<T>::max() / 4;
template<typename Real> constexpr Real pi_v = Real{3.141592653589793238462643383279502884};

template<typename T>
T read()
{
    T v;
    return std::cin >> v, v;
}
template<typename T, typename... Args>
auto read(const usize size, Args... args)
{
    std::vector<decltype(read<T>(args...))> ans(size);
    for (usize i = 0; i < size; i++) { ans[i] = read<T>(args...); }
    return ans;
}
template<typename... Types>
auto reads() { return std::tuple<std::decay_t<Types>...>{read<Types>()...}; }
#    define SHOW(...) static_cast<void>(0)
template<typename T>
T make_v(const T v) { return v; }
template<typename... Args>
auto make_v(const std::size_t size, Args... args) { return std::vector<decltype(make_v(args...))>(size, make_v(args...)); }


namespace bbst_node {
template<typename Key, typename Node, typename Comp>
struct key_node : Node
{
    using ptr       = key_node* const;
    using const_ptr = const ptr;
    using key_type  = Key;
    using comp_type = Comp;
    key_node() : Node{}, key{Key{}} {}
    template<typename... Args>
    key_node(const Key& key, Args... args) : Node{args...}, key{key} { this->sz = 1; }
    void pull_up(const_ptr l, const_ptr r) { Node::pull_up(l, r); }
    void push_down(ptr l, ptr r) { Node::push_down(l, r); }
    template<typename Value>
    void set(const Value& val, const_ptr l, const_ptr r) { Node::set(val, l, r); }
    template<typename Op>
    void act(const Op& o) { Node::act(o); }
    friend std::ostream& operator<<(std::ostream& os, const key_node& n) { return os << "key=" << n.key << ":" << static_cast<Node>(n); }
    const key_type key;
};
struct node
{
    using ptr       = node* const;
    using const_ptr = const ptr;
    void pull_up(const_ptr l, const_ptr r) { sz = (l ? l->sz : 0UL) + 1UL + (r ? r->sz : 0UL); }
    void push_down(ptr, ptr) {}
    friend std::ostream& operator<<(std::ostream& os, const node& n) { return os << "size=" << n.sz; }
    usize sz = 0;
};
template<typename Value>
struct value_node
{
    using ptr        = value_node* const;
    using const_ptr  = const ptr;
    using value_type = Value;
    value_node()     = default;
    value_node(const value_type& value) : value{value}, sz{1} {}
    void pull_up(const_ptr l, const_ptr r) { sz = (l ? l->sz : 0UL) + 1UL + (r ? r->sz : 0UL); }
    void push_down(ptr, ptr) {}
    void set(const value_type& val, const_ptr, const_ptr) { value = val; }
    friend std::ostream& operator<<(std::ostream& os, const value_node& n) { return os << "value=" << n.value; }
    value_type value{};
    usize sz = 0;
};
template<typename ValueMonoid>
struct merge_node
{
    using ptr               = merge_node* const;
    using const_ptr         = const ptr;
    using value_monoid_type = ValueMonoid;
    using value_type        = typename value_monoid_type::value_type;
    merge_node()            = default;
    merge_node(const value_type& value) : value{value}, merged{value}, sz{1} {}
    void pull_up(const_ptr l, const_ptr r) { sz = (l ? l->sz : 0UL) + 1UL + (r ? r->sz : 0UL), merged = value_monoid_type::merge((l ? l->merged : value_monoid_type::id()), value_monoid_type::merge(value, (r ? r->merged : value_monoid_type::id()))); }
    void push_down(ptr, ptr) {}
    void set(const value_type& val, const_ptr l, const_ptr r) { value = val, pull_up(l, r); }
    friend std::ostream& operator<<(std::ostream& os, const merge_node& n) { return os << "value=" << n.value << ",merged=" << n.merged; }
    value_type value = value_monoid_type::id(), merged = value_monoid_type::id();
    usize sz = 0;
};
template<typename MonoidAct>
struct lazy_node
{
    using ptr                  = lazy_node* const;
    using const_ptr            = const ptr;
    using monoid_act_type      = MonoidAct;
    using value_monoid_type    = typename monoid_act_type::value_monoid_type;
    using operator_monoid_type = typename monoid_act_type::operator_monoid_type;
    using value_type           = typename value_monoid_type::value_type;
    using operator_type        = typename operator_monoid_type::operator_type;
    lazy_node()                = default;
    lazy_node(const value_type& value) : value{value}, merged{value}, sz{1} {}
    void pull_up(const_ptr l, const_ptr r) { sz = (l ? l->sz : 0UL) + 1UL + (r ? r->sz : 0UL), merged = value_monoid_type::merge((l ? l->merged : value_monoid_type::id()), value_monoid_type::merge(value, (r ? r->merged : value_monoid_type::id()))); }
    void push_down(ptr l, ptr r)
    {
        if (op == operator_monoid_type::id()) { return; }
        if (l) { l->act(op); }
        if (r) { r->act(op); }
        op = operator_monoid_type::id();
    }
    void set(const value_type& val, const_ptr l, const_ptr r) { value = val, pull_up(l, r); }
    void act(const operator_type& o) { value = monoid_act_type::apply(o, value, 1), merged = monoid_act_type::apply(o, merged, sz), op = operator_monoid_type::compose(op, o); }
    friend std::ostream& operator<<(std::ostream& os, const lazy_node& n) { return os << "value=" << n.value << ",merged=" << n.merged << ",op=" << n.op; }
    value_type value = value_monoid_type::id(), merged = value_monoid_type::id();
    operator_type op = operator_monoid_type::id();
    usize sz         = 0;
};
}  // namespace bbst_node
template<typename NodeData>
class base_splaytree
{
private:
    class node
    {
        using ptr       = node*;
        using const_ptr = const node* const;
        using tree      = ptr;

    public:
        node() : node_data{} {}
        template<typename... Args>
        node(Args... args) : node_data{args...} {}
        usize size() const { return node_data.sz; }
        const NodeData& data() const { return node_data; }
        template<typename Operator>
        void act(const Operator& op) { node_data.act(op); }
        template<typename Value>
        void set(const Value& value) { node_data.set(value, data_ptr_of(l), data_ptr_of(r)), pull_up(); }
        friend std::ostream& operator<<(std::ostream& os, const node& n) { return os << "[" << n.node_data << "]"; }
        bool has_left() const { return l; }
        bool has_right() const { return r; }
        bool has_parent() const { return p; }
        const node& left() const { return deptr(l); }
        const node& right() const { return deptr(r); }
        const node& parent() const { return deptr(p); }
        static node& deptr(ptr x) { return x ? (*x) : empty_node; }
        static ptr merge(tree tp1, tree tp2)
        {
            if (not tp1) { return tp2; }
            if (not tp2) { return tp1; }
            ptr lp2    = kth_ptr(tp2, 0);
            return tp2 = (lp2->splay(), lp2), tp2->push_down(), tp2->l = tp1, tp1->p = tp2, tp2->pull_up(), tp2;
        }
        static std::pair<ptr, ptr> split_at(tree tp, const usize pos) { return split(tp, kth_ptr(tp, pos)); }
        static std::tuple<ptr, ptr, ptr> split_range(tree tp, const usize pos_min, const usize pos_sup)
        {
            auto ts = split_at(tp, pos_min), trs = split_at(ts.second, pos_sup - pos_min);
            return std::make_tuple(ts.first, trs.first, trs.second);
        }
        template<typename Key>
        static std::pair<ptr, ptr> split_lower(tree tp, const Key& key) { return split(tp, lower_bound(tp, key)); }
        template<typename Key>
        static std::pair<ptr, ptr> split_upper(tree tp, const Key& key) { return split(tp, upper_bound(tp, key)); }
        template<typename Key>
        static std::tuple<ptr, ptr, ptr> split_key_range(tree tp, const Key& key_min, const Key& key_max)
        {
            auto ts = split_lower(tp, key_min), trs = split_upper(ts.second, key_max);
            return std::make_tuple(ts.first, trs.first, trs.second);
        }

    private:
        static NodeData* data_ptr_of(ptr x) { return x ? &(x->node_data) : nullptr; }
        static usize size_of(const_ptr x) { return x ? x->size() : 0UL; }
        bool is_root() const { return (not p) or (p->l != this and p->r != this); }
        int is_left() const { return is_root() ? 0 : (p->l == this ? 1 : -1); }
        void pull_up() { node_data.pull_up(data_ptr_of(l), data_ptr_of(r)); }
        void push_down() { node_data.push_down(data_ptr_of(l), data_ptr_of(r)); }
        void rot()
        {
            ptr pp        = p->p;
            const int isl = p->is_left();
            if (is_left() == 1) {
                p->l = r, (r ? r->p : p) = p, r = p, p->p = this;
            } else {
                p->r = l, (l ? l->p : p) = p, l = p, p->p = this;
            }
            p->pull_up(), pull_up();
            p = pp;
            if (isl == 0) { return; }
            (isl == 1 ? pp->l : pp->r) = this, pp->pull_up();
        }
        void splay()
        {
            while (not is_root()) { (p->is_root() ? rot() : is_left() == p->is_left() ? (p->rot(), rot()) : (rot(), rot())); }
        }
        static std::pair<ptr, ptr> split(tree tp, ptr p)
        {
            if (not p) { return {tp, nullptr}; }
            tp     = (p->splay(), p);
            ptr lp = tp->l;
            if (not lp) { return std::make_pair(nullptr, tp); }
            return tp->push_down(), lp->p = nullptr, tp->l = nullptr, tp->pull_up(), std::make_pair(lp, tp);
        }
        static ptr kth_ptr(const tree tp, usize k)
        {
            for (ptr p = tp; p;) {
                p->push_down();
                const usize ind = size_of(p->l);
                if (ind == k) { return p; }
                p = (k < ind ? p->l : (k -= (ind + 1), p->r));
            }
            return nullptr;
        }
        template<typename Key>
        static ptr lower_bound(const tree tp, const Key& key)
        {
            static typename NodeData::comp_type comp{};
            ptr ans = nullptr;
            for (ptr p = tp; p;) { p->push_down(), p = (comp(p->data().key, key) ? p->r : (ans = p, p->l)); }
            return ans;
        }
        template<typename Key>
        static ptr upper_bound(const tree tp, const Key& key)
        {
            static typename NodeData::comp_type comp{};
            ptr ans = nullptr;
            for (ptr p = tp; p;) { p->push_down(), p = (comp(key, p->data().key) ? (ans = p, p->l) : p->r); }
            return ans;
        }
        static node empty_node;  // inline変数を使いたいでござる
        NodeData node_data;
        ptr l = nullptr, r = nullptr, p = nullptr;
    };
    using ptr       = node*;
    using const_ptr = const node* const;
    ptr root        = nullptr;

public:
    base_splaytree() {}
    base_splaytree(const ptr r) : root{r} {}
    template<typename... Args>
    base_splaytree(Args... args) : root{new node{args...}} {}
    bool empty() const { return not root; }
    usize size() const { return root ? root->sz : 0UL; }
    const node& top() const { return node::deptr(root); }
    const node at(const usize pos) { return fold_range(pos, pos + 1); }
    const node fold_range(const usize pos_min, const usize pos_sup)
    {
        auto ts        = node::split_range(root, pos_min, pos_sup);
        const node ans = node::deptr(std::get<1>(ts));
        return root    = node::merge(std::get<0>(ts), node::merge(std::get<1>(ts), std::get<2>(ts))), ans;
    }
    template<typename Key>
    const node fold_key_range(const Key& key_min, const Key& key_max)
    {
        auto ts        = node::split_key_range(root, key_min, key_max);
        const node ans = node::deptr(std::get<1>(ts));
        return root    = node::merge(std::get<0>(ts), node::merge(std::get<1>(ts), std::get<2>(ts))), ans;
    }
    template<typename Key>
    const node fold_lower(const Key& key)
    {
        auto ts        = node::split_lower(root, key);
        const node ans = node::deptr(ts.first);
        return root    = node::merge(ts.first, ts.second), ans;
    }
    template<typename Key>
    const node fold_upper(const Key& key)
    {
        auto ts        = node::split_upper(root, key);
        const node ans = node::deptr(ts.second);
        return root    = node::merge(ts.first, ts.second), ans;
    }
    template<typename Value>
    base_splaytree& set_at(const usize pos, const Value& value)
    {
        auto ts = node::split_range(root, pos, pos + 1);
        std::get<1>(ts)->set(value);
        return root = node::merge(std::get<0>(ts), node::merge(std::get<1>(ts), std::get<2>(ts))), *this;
    }
    template<typename Key, typename Value>
    base_splaytree& set(const Key& key, const Value& value)
    {
        auto ts = node::split_key_range(root, key, key);
        std::get<1>(ts)->set(value);
        return root = node::merge(std::get<0>(ts), node::merge(std::get<1>(ts), std::get<2>(ts))), *this;
    }
    template<typename Op>
    base_splaytree& act_range(const usize pos_min, const usize pos_sup, const Op& op)
    {
        auto ts = node::split_range(root, pos_min, pos_sup);
        std::get<1>(ts)->act(op);
        return root = node::merge(std::get<0>(ts), node::merge(std::get<1>(ts), std::get<2>(ts))), *this;
    }
    template<typename Key, typename Op>
    base_splaytree& act_key_range(const Key& key_min, const Key& key_max, const Op& op)
    {
        auto ts = node::split_key_range(root, key_min, key_max);
        std::get<1>(ts)->act(op);
        return root = node::merge(std::get<0>(ts), node::merge(std::get<1>(ts), std::get<2>(ts))), *this;
    }
    base_splaytree& merge(base_splaytree&& t) { return root = node::merge(root, t.root), *this; }
    base_splaytree split_at(const usize pos)
    {
        auto ts     = node::split_at(root, pos);
        return root = ts.first, base_splaytree(ts.second);
    }
    std::pair<base_splaytree, base_splaytree> split_range(const usize pos_min, const usize pos_sup)
    {
        auto ts     = node::split_range(root, pos_min, pos_sup);
        return root = std::get<0>(ts), std::make_pair(base_splaytree(std::get<1>(ts)), base_splaytree(std::get<2>(ts)));
    }
    base_splaytree& erase_at(const usize pos)
    {
        auto ts = node::split_at(root, pos), trs = node::split_at(ts.second, 1);
        return root = node::merge(ts.first, trs.second), *this;
    }
    base_splaytree& insert_at(const usize pos, base_splaytree&& t)
    {
        auto ts     = node::split_at(root, pos);
        return root = node::merge(node::merge(ts.first, t.root), ts.second), *this;
    }
    template<typename Key>
    base_splaytree split_lower(const Key& key)
    {
        auto ts     = node::split_lower(root, key);
        return root = ts.first, base_splaytree(ts.second);
    }
    template<typename Key>
    base_splaytree split_upper(const Key& key)
    {
        auto ts     = node::split_upper(root, key);
        return root = ts.first, base_splaytree(ts.second);
    }
    template<typename Key>
    std::pair<base_splaytree, base_splaytree> split_key_range(const Key& key_min, const Key& key_max)
    {
        auto ts     = node::split_key_range(root, key_min, key_max);
        return root = std::get<0>(ts), std::make_pair(base_splaytree(std::get<1>(ts)), base_splaytree(std::get<2>(ts)));
    }
    base_splaytree& insert(const node& n)
    {
        auto ts     = node::split_lower(root, n.data().key);
        return root = node::merge(node::merge(ts.first, new node{n}), ts.second), *this;
    }
    std::vector<node> data() const
    {
        if (empty()) { return std::vector<node>{}; }
        auto dfs = [&](auto&& self, const node& n) -> std::vector<node> {
            std::vector<node> ans;
            if (n.has_left()) {
                for (auto&& e : self(self, n.left())) { ans.emplace_back(e); }
            }
            ans.push_back(n);
            if (n.has_right()) {
                for (auto&& e : self(self, n.right())) { ans.emplace_back(e); }
            }
            return ans;
        };
        return dfs(dfs, *root);
    }
};
template<typename NodeData>
typename base_splaytree<NodeData>::node base_splaytree<NodeData>::node::empty_node = node{};
template<typename Value>
using splaytree = base_splaytree<bbst_node::value_node<Value>>;
template<typename Key, typename Comp = std::less<Key>>
using mset_splaytree = base_splaytree<bbst_node::key_node<Key, bbst_node::node, Comp>>;
template<typename Key, typename Value, typename Comp = std::less<Key>>
using mmap_splaytree = base_splaytree<bbst_node::key_node<Key, bbst_node::value_node<Value>, Comp>>;
template<typename ValueMonoid>
using merge_splaytree = base_splaytree<bbst_node::merge_node<ValueMonoid>>;
template<typename MonoidAct>
using lazy_splaytree = base_splaytree<bbst_node::lazy_node<MonoidAct>>;

class segments
{
private:
    using P = std::pair<usize, usize>;
    const usize ceil;
    std::vector<P> rs;
    const usize num;  // 区間0は存在しないので、実際は区間1,2,...,num-1

public:
    segments(const usize sz) : ceil{ceil2(sz)}, rs(ceil << 1, P{0, 0}), num{ceil << 1}
    {
        for (usize sz = 1; sz <= ceil; sz <<= 1) {
            const usize len = ceil / sz;
            for (usize j = sz; j < (sz << 1); j++) { rs[j] = {len * (j - sz), len * (j - sz + 1)}; }
        }
    }
    std::vector<usize> under(usize l, usize r) const
    {
        assert(l < r), assert(r <= ceil);
        std::vector<usize> lind, rind;
        for (l += ceil, r += ceil; l < r; l >>= 1, r >>= 1) {
            if (l & 1) { lind.push_back(l++); }
            if (r & 1) { rind.push_back(--r); }
        }
        for (; not rind.empty(); rind.pop_back()) { lind.push_back(rind.back()); }
        return lind;
    }
    std::vector<usize> over(const usize a) const
    {
        assert(a < ceil);
        std::vector<usize> ans;
        for (usize i = a + ceil; i >= 1; i >>= 1) { ans.push_back(i); }
        std::reverse(ans.begin(), ans.end());
        return ans;
    }
    usize max_index() const { return num; }
    const P& operator[](const usize i) const
    {
        assert(i >= 1), assert(i < 2 * ceil);
        return rs[i];
    }
};
//#include "data_structure/dynamic_wavelet.hpp"
template<typename Element>
struct plus
{
    using element_type  = Element;
    using operator_type = element_type;
    plus()              = delete;
    static operator_type compose(const operator_type& a, const operator_type& b) { return a + b; }
    static constexpr operator_type id() { return operator_type{}; }
};
template<typename Element>
struct sum
{
    using element_type = Element;
    using value_type   = element_type;
    sum()              = delete;
    static value_type merge(const value_type& a, const value_type& b) { return a + b; }
    static constexpr value_type id() { return value_type{}; }
};
template<typename ValueElement, typename OperatorElement>
struct sum_plus
{
    using value_element_type    = ValueElement;
    using operator_element_type = OperatorElement;
    using value_monoid_type     = sum<value_element_type>;
    using operator_monoid_type  = plus<operator_element_type>;
    using value_type            = typename value_monoid_type::value_type;
    using operator_type         = typename operator_monoid_type::operator_type;
    sum_plus()                  = delete;
    template<typename Ind>
    static value_type apply(const operator_type& f, const value_type& x, const Ind l) { return x + static_cast<value_type>(l) * static_cast<value_type>(f); }
};
enum {
    NOTFOUND = 0xFFFFFFFFFFFFFFFFLLU
};

uint64_t NODE_NO = 0;

class Node
{
public:
    uint64_t no;  // node番号

    // internal nodeのときに使用
    uint64_t num;   // 左の子の部分木のもつbitの数
    uint64_t ones;  // 左の子の部分木のもつ1の数
    Node* left;
    Node* right;
    int64_t balance;  // 右の子の高さ - 左の子の高さ．+なら右の子の方が高い，-なら左の子の方が高い

    // leafのときに使用
    uint64_t bits;       // bit
    uint64_t bits_size;  // bitのサイズ(debug用)

    bool is_leaf;

    Node(uint64_t bits, uint64_t bits_size, bool is_leaf) : no(NODE_NO++), num(0), ones(0), bits(bits), bits_size(bits_size), is_leaf(is_leaf), left(nullptr), right(nullptr), balance(0) {}
};

class DynamicBitVector
{
public:
    Node* root;
    uint64_t size;                        // 全体のbitの数
    uint64_t num_one;                     // 全体の1の数
    const uint64_t bits_size_limit = 32;  // 各ノードが管理するbitの長さ制限．2 * bits_size_limit以上になったらノードを分割し， 1/2*bits_size_limit以下になったらノードを結合する

    DynamicBitVector() : root(nullptr), size(0), num_one(0) {}

    DynamicBitVector(std::vector<uint64_t>& v) : root(nullptr), size(0), num_one(0)
    {
        if (v.size() == 0) {
            return;
        }

        std::deque<std::pair<Node*, uint64_t>> leaves;
        for (int i = 0; i < v.size(); i += this->bits_size_limit) {
            uint64_t bits            = 0;
            const uint64_t bits_size = std::min(this->bits_size_limit, (uint64_t)v.size() - i);
            for (int j = 0; j < bits_size; ++j) {
                assert(v[i + j] == 0 or v[i + j] == 1);
                if (v[i + j] == 1) {
                    bits |= (uint64_t)1 << j;
                }
            }

            leaves.emplace_back(std::make_pair(new Node(bits, bits_size, true), bits_size));
        }

        std::deque<std::tuple<Node*, uint64_t, uint64_t, uint64_t>> nodes;  // (node, 全体のbit数, 全体の1の数, 高さ)
        while (not leaves.empty()) {
            const auto node      = leaves.front().first;
            const auto bits_size = leaves.front().second;
            leaves.pop_front();
            nodes.emplace_back(std::make_tuple(node, bits_size, popCount(node->bits), 0));
        }

        while (nodes.size() > 1) {
            std::deque<std::tuple<Node*, uint64_t, uint64_t, uint64_t>> next_nodes;
            while (not nodes.empty()) {
                // あまりがでたときは，最後に作った中間ノードと結合させるためにnodesに戻す
                if (nodes.size() == 1) {
                    nodes.push_front(next_nodes.back());
                    next_nodes.pop_back();
                }

                Node* left_node;
                uint64_t left_num, left_ones, left_height;
                std::tie(left_node, left_num, left_ones, left_height) = nodes.front();
                nodes.pop_front();

                Node* right_node;
                uint64_t right_num, right_ones, right_height;
                std::tie(right_node, right_num, right_ones, right_height) = nodes.front();
                nodes.pop_front();

                const auto internal_node = new Node(0, 0, false);
                internal_node->num       = left_num;
                internal_node->ones      = left_ones;
                internal_node->left      = left_node;
                internal_node->right     = right_node;
                internal_node->balance   = right_height - left_height;

                next_nodes.emplace_back(std::make_tuple(internal_node, left_num + right_num, left_ones + right_ones, std::max(left_height, right_height) + 1));
            }

            nodes = next_nodes;
        }

        uint64_t height;
        std::tie(this->root, this->size, this->num_one, height) = nodes.front();
        nodes.pop_front();
        assert(this->size == v.size());
    }

    // B[pos]
    uint64_t access(uint64_t pos)
    {
        assert(pos < this->size);

        return access(this->root, pos);
    }

    // B[0, pos)にある指定されたbitの数
    uint64_t rank(uint64_t bit, uint64_t pos)
    {
        assert(bit == 0 or bit == 1);
        assert(pos <= this->size);

        if (bit) {
            return rank1(this->root, pos, 0);
        } else {
            return pos - rank1(this->root, pos, 0);
        }
    }

    // rank番目の指定されたbitの位置 + 1(rankは1-origin)
    uint64_t select(uint64_t bit, uint64_t rank)
    {
        assert(bit == 0 or bit == 1);
        assert(rank > 0);

        if (bit == 0 and rank > this->size - this->num_one) { return NOTFOUND; }
        if (bit == 1 and rank > this->num_one) { return NOTFOUND; }

        if (bit) {
            return select1(this->root, 0, rank);
        } else {
            return select0(this->root, 0, rank);
        }
    }

    // posにbitを挿入する
    void insert(uint64_t pos, uint64_t bit)
    {
        assert(bit == 0 or bit == 1);
        assert(pos <= this->size);  // 現在もってるbitsの末尾には挿入できる

        if (root == nullptr) {
            root = new Node(bit, 1, true);
        } else {
            insert(this->root, nullptr, bit, pos, this->size);
        }
        this->size++;
        this->num_one += (bit == 1);
    }

    // posを削除する
    void erase(uint64_t pos)
    {
        assert(pos < this->size);

        uint64_t bit = this->remove(this->root, nullptr, pos, this->size, 0, true).first;
        this->size--;
        this->num_one -= (bit == 1);
    }

private:
    uint64_t access(const Node* node, uint64_t pos)
    {
        if (node->is_leaf) {
            assert(pos <= 2 * this->bits_size_limit);
            return (node->bits >> pos) & (uint64_t)1;
        }

        if (pos < node->num) {
            return this->access(node->left, pos);
        } else {
            return this->access(node->right, pos - node->num);
        }
    }

    uint64_t rank1(const Node* node, uint64_t pos, uint64_t ones)
    {
        if (node->is_leaf) {
            assert(node->bits_size >= pos);
            const uint64_t mask = ((uint64_t)1 << pos) - 1;
            return ones + popCount(node->bits & mask);
        }

        if (pos < node->num) {
            return this->rank1(node->left, pos, ones);
        } else {
            return this->rank1(node->right, pos - node->num, ones + node->ones);
        }
    }

    uint64_t select1(const Node* node, uint64_t pos, uint64_t rank)
    {
        if (node->is_leaf) {
            return pos + this->selectInBlock(node->bits, rank) + 1;
        }

        if (rank <= node->ones) {
            return this->select1(node->left, pos, rank);
        } else {
            return this->select1(node->right, pos + node->num, rank - node->ones);
        }
    }

    uint64_t select0(const Node* node, uint64_t pos, uint64_t rank)
    {
        if (node->is_leaf) {
            return pos + this->selectInBlock(~node->bits, rank) + 1;
        }

        if (rank <= (node->num - node->ones)) {
            return this->select0(node->left, pos, rank);
        } else {
            return this->select0(node->right, pos + node->num, rank - (node->num - node->ones));
        }
    }

    // bits(64bit)のrank番目(0-index)の1の数
    uint64_t selectInBlock(uint64_t bits, uint64_t rank)
    {
        const uint64_t x1 = bits - ((bits & 0xAAAAAAAAAAAAAAAALLU) >> (uint64_t)1);
        const uint64_t x2 = (x1 & 0x3333333333333333LLU) + ((x1 >> (uint64_t)2) & 0x3333333333333333LLU);
        const uint64_t x3 = (x2 + (x2 >> (uint64_t)4)) & 0x0F0F0F0F0F0F0F0FLLU;

        uint64_t pos = 0;
        for (;; pos += 8) {
            const uint64_t rank_next = (x3 >> pos) & 0xFFLLU;
            if (rank <= rank_next) break;
            rank -= rank_next;
        }

        const uint64_t v2 = (x2 >> pos) & 0xFLLU;
        if (rank > v2) {
            rank -= v2;
            pos += 4;
        }

        const uint64_t v1 = (x1 >> pos) & 0x3LLU;
        if (rank > v1) {
            rank -= v1;
            pos += 2;
        }

        const uint64_t v0 = (bits >> pos) & 0x1LLU;
        if (v0 < rank) {
            pos += 1;
        }

        return pos;
    }

    // nodeから辿れる葉のpos番目にbitをいれる(葉のbitの長さはlen)
    // 高さの変化を返す
    int64_t insert(Node* node, Node* parent, uint64_t bit, uint64_t pos, uint64_t len)
    {
        assert(bit == 0 or bit == 1);
        if (node->is_leaf) {
            assert(pos <= 2 * this->bits_size_limit);

            // posより左をとりだす
            const uint64_t up_mask = (((uint64_t)1 << (len - pos)) - 1) << pos;
            const uint64_t up      = (node->bits & up_mask);

            // posより右をとりだす
            const uint64_t down_mask = ((uint64_t)1 << pos) - 1;
            const uint64_t down      = node->bits & down_mask;

            node->bits = (up << (uint64_t)1) | (bit << pos) | down;
            node->bits_size++;
            assert(node->bits_size == len + 1);

            // bitsのサイズが大きくなったので分割する
            if (len + 1 >= 2 * bits_size_limit) {
                this->splitNode(node, len + 1);  // 引数のlenはinsert後の長さなので+1する
                return 1;
            }

            return 0;
        }

        if (pos < node->num) {
            const int64_t diff = this->insert(node->left, node, bit, pos, node->num);
            node->num += 1;
            node->ones += (bit == 1);
            return achieveBalance(parent, node, diff, 0);
        } else {
            const int64_t diff = this->insert(node->right, node, bit, pos - node->num, len - node->num);
            return achieveBalance(parent, node, 0, diff);
        }
    }

    // nodeのpos番目のbitを削除する
    // 消したbitと高さの変化のpairを返す
    std::pair<uint64_t, int64_t> remove(Node* node, Node* parent, uint64_t pos, uint64_t len, uint64_t ones, bool allow_under_flow)
    {
        if (node->is_leaf) {
            // 消すとunder flowになるので消さない
            if (node != this->root and len <= bits_size_limit / 2 and not allow_under_flow) {
                return std::make_pair(NOTFOUND, 0);
            }

            assert(pos <= 2 * this->bits_size_limit);
            assert(pos < len);
            const uint64_t bit = (node->bits >> pos) & (uint64_t)1;

            // posより左をとりだす(posを含まないようにする)
            const uint64_t up_mask = (((uint64_t)1 << (len - pos - 1)) - 1) << (pos + 1);
            const uint64_t up      = (node->bits & up_mask);

            // posより右をとりだす
            const uint64_t down_mask = ((uint64_t)1 << pos) - 1;
            const uint64_t down      = node->bits & down_mask;

            node->bits = (up >> (uint64_t)1) | down;
            node->bits_size--;
            assert(node->bits_size == len - 1);

            return std::make_pair(bit, 0);
        }

        if (pos < node->num) {
            const auto bit_diff = this->remove(node->left, node, pos, node->num, node->ones, allow_under_flow);
            if (bit_diff.first == NOTFOUND) {
                return bit_diff;
            }

            node->ones -= (bit_diff.first == 1);
            // 左の子の葉のbitを1つ消したのでunder flowが発生している
            if (node->num == bits_size_limit / 2) {
                const auto b_d = remove(node->right, node, 0, len - bits_size_limit / 2, 0, false);  // 右の葉の先頭bitを削る

                // 右の葉もunder flowになって消せない場合は2つの葉を統合する
                if (b_d.first == NOTFOUND) {
                    assert(node->left->is_leaf);
                    assert(node->left->bits_size == bits_size_limit / 2 - 1);
                    // 右の子から辿れる一番左の葉の先頭にleftのbitsを追加する
                    mergeNodes(node->right, 0, len - bits_size_limit / 2, node->left->bits, bits_size_limit / 2 - 1, node->ones, true);
                    this->replace(parent, node, node->right);  // parentの子のnodeをnode->rightに置き換える
                    return std::make_pair(bit_diff.first, -1);
                }

                // 右の葉からとった先頭bitを左の葉の末尾にいれる
                assert(node->left->bits_size == bits_size_limit / 2 - 1);
                insert(node->left, node, b_d.first, bits_size_limit / 2 - 1, bits_size_limit / 2 - 1);
                node->ones += (b_d.first == 1);
            } else {
                node->num -= 1;
            }

            const int64_t diff = achieveBalance(parent, node, bit_diff.second, 0);
            return std::make_pair(bit_diff.first, diff);

        } else {
            const auto bit_diff = this->remove(node->right, node, pos - node->num, len - node->num, ones - node->ones, allow_under_flow);
            if (bit_diff.first == NOTFOUND) {
                return bit_diff;
            }

            ones -= (bit_diff.first == 1);
            // 右の子の葉のbitを1つ消したのでunder flowが発生する
            if ((len - node->num) == bits_size_limit / 2) {
                const auto b_d = remove(node->left, node, node->num - 1, node->num, 0, false);  // 左の葉の末尾をbitを削る

                // 左の葉もunder flowになって消せない場合は2つの葉を統合する
                if (b_d.first == NOTFOUND) {
                    assert(node->right->is_leaf);
                    assert(node->right->bits_size == bits_size_limit / 2 - 1);
                    // 左の子から辿れる一番右の葉の末尾にleftのbitsを追加する
                    mergeNodes(node->left, node->num, node->num, node->right->bits, bits_size_limit / 2 - 1, ones - node->ones, false);
                    this->replace(parent, node, node->left);  // parentの子のnodeをnode->leftに置き換える
                    return std::make_pair(bit_diff.first, -1);
                }

                // 左の葉からとった最後尾bitを右の葉の先頭にいれる
                insert(node->right, node, b_d.first, 0, bits_size_limit / 2 - 1);
                node->num -= 1;
                node->ones -= (b_d.first == 1);
            }

            const int64_t diff = achieveBalance(parent, node, 0, bit_diff.second);
            return std::make_pair(bit_diff.first, diff);
        }
    }

    // nodeを2つの葉に分割する
    void splitNode(Node* node, uint64_t len)
    {
        assert(node->is_leaf);
        assert(node->bits_size == len);

        // 左の葉
        const uint64_t left_size = len / 2;
        const uint64_t left_bits = node->bits & (((uint64_t)1 << left_size) - 1);
        node->left               = new Node(left_bits, left_size, true);

        // 右の葉
        const uint64_t right_size = len - left_size;
        const uint64_t right_bits = node->bits >> left_size;
        node->right               = new Node(right_bits, right_size, true);

        // nodeを内部ノードにする
        node->is_leaf   = false;
        node->num       = left_size;
        node->ones      = this->popCount(left_bits);
        node->bits      = 0;
        node->bits_size = 0;
    }

    // nodeから辿れる葉のpos番目にbitsを格納する
    void mergeNodes(Node* node, uint64_t pos, uint64_t len, uint64_t bits, uint64_t s, uint64_t ones, bool left)
    {
        if (node->is_leaf) {
            if (left) {
                node->bits = (node->bits << s) | bits;
            } else {
                assert(len == node->bits_size);
                node->bits = node->bits | (bits << len);
            }
            node->bits_size += s;
            return;
        }

        if (pos < node->num) {
            node->num += s;
            node->ones += ones;
            mergeNodes(node->left, pos, node->num, bits, s, ones, left);
        } else {
            mergeNodes(node->right, pos, len - node->num, bits, s, ones, left);
        }
    }

    // nodeの左の高さがleftHeightDiffだけ変わり，右の高さがrightHeightDiffだけ変わったときにnodeを中心に回転させる
    // 高さの変化を返す
    int64_t achieveBalance(Node* parent, Node* node, int64_t leftHeightDiff, int64_t rightHeightDiff)
    {
        assert(-1 <= node->balance and node->balance <= 1);
        assert(-1 <= leftHeightDiff and leftHeightDiff <= 1);
        assert(-1 <= rightHeightDiff and rightHeightDiff <= 1);

        if (leftHeightDiff == 0 and rightHeightDiff == 0) {
            return 0;
        }

        int64_t heightDiff = 0;
        // 左が高いときに，左が高くなる or 右が高いときに右が高くなる
        if ((node->balance <= 0 and leftHeightDiff > 0) or (node->balance >= 0 and rightHeightDiff > 0)) {
            ++heightDiff;
        }
        // 左が高いときに左が低くなる or 右が高いときに右が低くなる
        if ((node->balance < 0 and leftHeightDiff < 0) or (node->balance > 0 and rightHeightDiff < 0)) {
            --heightDiff;
        }

        node->balance += -leftHeightDiff + rightHeightDiff;
        assert(-2 <= node->balance and node->balance <= 2);

        // 左が2高い
        if (node->balance == -2) {
            assert(-1 <= node->left->balance and node->left->balance <= 1);
            if (node->left->balance != 0) {
                heightDiff--;
            }

            if (node->left->balance == 1) {
                replace(node, node->left, rotateLeft(node->left));
            }
            replace(parent, node, rotateRight(node));
        }
        // 右が2高い
        else if (node->balance == 2) {
            assert(-1 <= node->right->balance and node->right->balance <= 1);
            if (node->right->balance != 0) {
                heightDiff--;
            }

            if (node->right->balance == -1) {
                replace(node, node->right, rotateRight(node->right));
            }
            replace(parent, node, rotateLeft(node));
        }

        return heightDiff;
    }

    // node Bを中心に左回転する．新しい親を返す
    Node* rotateLeft(Node* B)
    {
        Node* D = B->right;

        const int64_t heightC = 0;
        const int64_t heightE = heightC + D->balance;
        const int64_t heightA = std::max(heightC, heightE) + 1 - B->balance;

        B->right = D->left;
        D->left  = B;

        B->balance = heightC - heightA;
        D->num += B->num;
        D->ones += B->ones;
        D->balance = heightE - (std::max(heightA, heightC) + 1);

        assert(-2 <= B->balance and B->balance <= 2);
        assert(-2 <= D->balance and D->balance <= 2);

        return D;
    }

    // node Dを中心に右回転する．新しい親を返す
    Node* rotateRight(Node* D)
    {
        Node* B = D->left;

        const int64_t heightC = 0;
        const int64_t heightA = heightC - B->balance;
        const int64_t heightE = std::max(heightA, heightC) + 1 + D->balance;

        D->left  = B->right;
        B->right = D;

        D->num -= B->num;
        D->ones -= B->ones;
        D->balance = heightE - heightC;
        B->balance = std::max(heightC, heightE) + 1 - heightA;

        assert(-2 <= B->balance and B->balance <= 2);
        assert(-2 <= D->balance and D->balance <= 2);

        return B;
    }

    // parentの子のoldNodeをnewNodeに置き換える
    void replace(Node* parent, Node* oldNode, Node* newNode)
    {
        if (parent == nullptr) {
            this->root = newNode;
            return;
        }

        if (parent->left == oldNode) {
            parent->left = newNode;
        } else if (parent->right == oldNode) {
            parent->right = newNode;
        } else {
            throw "old node is not child";
        }
    }

    uint64_t popCount(uint64_t x)
    {
        x = (x & 0x5555555555555555ULL) + ((x >> (uint64_t)1) & 0x5555555555555555ULL);
        x = (x & 0x3333333333333333ULL) + ((x >> (uint64_t)2) & 0x3333333333333333ULL);
        x = (x + (x >> (uint64_t)4)) & 0x0f0f0f0f0f0f0f0fULL;
        x = x + (x >> (uint64_t)8);
        x = x + (x >> (uint64_t)16);
        x = x + (x >> (uint64_t)32);
        return x & 0x7FLLU;
    }
};

class DynamicWaveletMatrix
{
public:
    std::vector<DynamicBitVector> bit_arrays;
    std::vector<uint64_t> begin_one;  // 各bitの1の開始位置

    uint64_t size;             // 与えられた配列のサイズ
    uint64_t maximum_element;  // 最大の文字
    uint64_t bit_size;         // 文字を表すのに必要なbit数

public:
    // max_element: 入ってくる中で一番大きい数値
    DynamicWaveletMatrix(uint64_t maximum_element) : size(0), maximum_element(maximum_element + 1)
    {
        this->bit_size = this->get_num_of_bit(maximum_element);
        if (bit_size == 0) {
            bit_size = 1;
        }
        this->begin_one.resize(bit_size);

        for (uint64_t i = 0; i < bit_size; ++i) {
            DynamicBitVector sv;
            bit_arrays.push_back(sv);
        }
    }

    DynamicWaveletMatrix(uint64_t num_of_alphabet, const std::vector<uint64_t>& array) : size(0), maximum_element(num_of_alphabet + 1)
    {
        this->bit_size = this->get_num_of_bit(num_of_alphabet);
        if (bit_size == 0) {
            bit_size = 1;
        }
        this->begin_one.resize(bit_size);

        if (array.size() == 0) {
            for (uint64_t i = 0; i < bit_size; ++i) {
                DynamicBitVector sv;
                bit_arrays.push_back(sv);
            }
            return;
        }

        size = array.size();

        std::vector<uint64_t> v(array), b(array.size(), 0);

        for (uint64_t i = 0; i < bit_size; ++i) {
            std::vector<uint64_t> temp;
            // 0をtempにいれてく
            for (uint64_t j = 0; j < v.size(); ++j) {
                uint64_t c   = v.at(j);
                uint64_t bit = (c >> (bit_size - i - 1)) & 1;  //　上からi番目のbit
                if (bit == 0) {
                    temp.push_back(c);
                    b[j] = 0;
                }
            }

            this->begin_one.at(i) = temp.size();

            // 1をtempにいれてく
            for (uint64_t j = 0; j < v.size(); ++j) {
                uint64_t c   = v.at(j);
                uint64_t bit = (c >> (bit_size - i - 1)) & 1;  //　上からi番目のbit
                if (bit == 1) {
                    temp.push_back(c);
                    b[j] = 1;
                }
            }

            DynamicBitVector dbv(b);
            bit_arrays.emplace_back(dbv);
            v = temp;
        }
    }

    // v[pos]
    uint64_t access(uint64_t pos)
    {
        if (pos >= this->size) { return NOTFOUND; }

        uint64_t c = 0;
        for (uint64_t i = 0; i < bit_arrays.size(); ++i) {
            uint64_t bit = bit_arrays.at(i).access(pos);  // もとの数値がのi番目のbit
            c            = (c <<= 1) | bit;
            pos          = bit_arrays.at(i).rank(bit, pos);
            if (bit) {
                pos += this->begin_one.at(i);
            }
        }
        return c;
    }

    // i番目のcの位置 + 1を返す。rankは1-origin
    uint64_t select(uint64_t c, uint64_t rank)
    {
        assert(rank > 0);
        if (c >= maximum_element) {
            return NOTFOUND;
        }

        uint64_t left = 0;
        for (uint64_t i = 0; i < bit_size; ++i) {
            const uint64_t bit = (c >> (bit_size - i - 1)) & 1;     // 上からi番目のbit
            left               = bit_arrays.at(i).rank(bit, left);  // cのi番目のbitと同じ数値の数
            if (bit) {
                left += this->begin_one.at(i);
            }
        }

        uint64_t index = left + rank;
        for (uint64_t i = 0; i < bit_arrays.size(); ++i) {
            uint64_t bit = ((c >> i) & 1);  // 下からi番目のbit
            if (bit == 1) {
                index -= this->begin_one.at(bit_size - i - 1);
            }
            index = this->bit_arrays.at(bit_size - i - 1).select(bit, index);
        }
        return index;
    }

    // posにcを挿入する
    void insert(uint64_t pos, uint64_t c)
    {
        assert(pos <= this->size);

        for (uint64_t i = 0; i < bit_arrays.size(); ++i) {
            const uint64_t bit = (c >> (bit_size - i - 1)) & 1;  //　上からi番目のbit
            bit_arrays.at(i).insert(pos, bit);
            pos = bit_arrays.at(i).rank(bit, pos);
            if (bit) {
                pos += this->begin_one.at(i);
            } else {
                this->begin_one.at(i)++;
            }
        }

        this->size++;
    }

    // posを削除する
    void erase(uint64_t pos)
    {
        assert(pos < this->size);
        if (pos >= this->size) {
            throw "Segmentation fault";
        }

        for (uint64_t i = 0; i < bit_arrays.size(); ++i) {
            uint64_t bit = bit_arrays.at(i).access(pos);  // もとの数値のi番目のbit

            auto next_pos = bit_arrays.at(i).rank(bit, pos);
            bit_arrays.at(i).erase(pos);

            if (bit) {
                next_pos += this->begin_one.at(i);
            } else {
                this->begin_one.at(i)--;
            }
            pos = next_pos;
        }
        this->size--;
    }

    // posにcをセットする
    void update(uint64_t pos, uint64_t c)
    {
        assert(pos < this->size);
        this->erase(pos);
        this->insert(pos, c);
    }

    // v[begin_pos, end_pos)で最小値のindexを返す
    uint64_t minRange(uint64_t begin_pos, uint64_t end_pos)
    {
        return quantileRange(begin_pos, end_pos, 0);
    }

    // v[begin_pos, end_pos)でk番目に小さい数値のindexを返す(kは0-origin)
    // つまり小さい順に並べてk番目の値
    uint64_t quantileRange(uint64_t begin_pos, uint64_t end_pos, uint64_t k)
    {
        if ((end_pos > size || begin_pos >= end_pos) || (k >= end_pos - begin_pos)) {
            return NOTFOUND;
        }

        uint64_t val = 0;
        for (uint64_t i = 0; i < bit_size; ++i) {
            uint64_t num_of_zero_begin = bit_arrays.at(i).rank(0, begin_pos);
            uint64_t num_of_zero_end   = bit_arrays.at(i).rank(0, end_pos);
            uint64_t num_of_zero       = num_of_zero_end - num_of_zero_begin;  // beginからendまでにある0の数
            uint64_t bit               = (k < num_of_zero) ? 0 : 1;            // k番目の値の上からi番目のbitが0か1か

            if (bit) {
                k -= num_of_zero;
                begin_pos = this->begin_one.at(i) + begin_pos - num_of_zero_begin;
                end_pos   = this->begin_one.at(i) + end_pos - num_of_zero_end;
            } else {
                begin_pos = num_of_zero_begin;
                end_pos   = num_of_zero_begin + num_of_zero;
            }

            val = ((val << 1) | bit);
        }

        uint64_t left = 0;
        for (uint64_t i = 0; i < bit_size; ++i) {
            const uint64_t bit = (val >> (bit_size - i - 1)) & 1;   // 上からi番目のbit
            left               = bit_arrays.at(i).rank(bit, left);  // cのi番目のbitと同じ数値の数
            if (bit) {
                left += this->begin_one.at(i);
            }
        }

        uint64_t rank = begin_pos + k - left + 1;
        return select(val, rank) - 1;
    }

private:
    uint64_t get_num_of_bit(uint64_t x)
    {
        if (x == 0) return 0;
        x--;
        uint64_t bit_num = 0;
        while (x >> bit_num) {
            ++bit_num;
        }
        return bit_num;
    }
};
int main()
{
    constexpr ull MAX = 1ULL << 40;
    using node        = bbst_node::key_node<ull, bbst_node::lazy_node<sum_plus<ull, ull>>, std::less<ull>>;
    using tree        = base_splaytree<node>;
    const auto [n, q] = reads<usize, usize>();
    auto a            = read<uint64_t>(n);
    DynamicWaveletMatrix wm((1UL << 40) - 1, a);
    auto median = [&](const usize l, const usize r) { return wm.access(wm.quantileRange(l, r, (r - l) / 2)); };

    const auto m = ceil2(n);
    std::vector<tree> sorted(2 * m);
    segments segs{n};
    for (usize i = 1; i < 2 * m; i++) {
        const auto [l, r] = segs[i];
        for (usize j = l; j < std::min(r, n); j++) { sorted[i].insert({a[j], a[j]}); }
    }

    ull s               = 0;
    constexpr ull pmask = (1ULL << 16) - 1, vmask = (1ULL << 40) - 1;
    for (usize i = 0; i < q; i++) {
        const usize t = read<usize>();
        if (t == 1) {
            const usize sp = s & pmask;
            const ull sv   = s & vmask;
            const auto x   = (read<usize>() ^ (sp)) - 1;
            const auto y   = (read<ull>() ^ sv);
            for (const usize i : segs.over(x)) {
                auto& lst       = sorted[i];
                auto [mst, rst] = lst.split_key_range(a[x], a[x]);
                auto mst2       = mst.split_at(1);
                mst2.merge(std::move(rst));
                lst.merge(std::move(mst2));
                lst.insert({y, y});
            }
            wm.update(x, y), a[x] = y;
        } else {
            const usize sp = s & pmask;
            auto l = (read<usize>() ^ (sp)), r = (read<usize>() ^ (sp));
            if (l > r) { std::swap(l, r); }
            l--;
            const ll m = median(l, r);
            SHOW(l, r, m);
            ll ans = 0;
            for (const usize i : segs.under(l, r)) {
                auto& lst     = sorted[i];
                auto rst      = sorted[i].split_lower(m);
                const usize l = lst.top().data().sz;
                const usize r = rst.top().data().sz;
                const ll lsum = (ll)l * m - lst.top().data().merged;
                const ll rsum = rst.top().data().merged - (ll)r * m;
                ans += (lsum + rsum);
                lst.merge(std::move(rst));
            }
            s ^= ans;
            std::cout << ans << std::endl;
        }
    }
    return 0;
}