/**
 * date   : 2024-02-25 03:30:28
 * author : Nyaan
 */

#define NDEBUG

using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility

namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  template <typename S>
  P &operator*=(const S &r) {
    first *= r, second *= r;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
  template <typename S>
  P operator*(const S &r) const {
    return P(*this) *= r;
  }
  P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

vector<int> mkiota(int n) {
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
T mkrev(const T &v) {
  T w{v};
  reverse(begin(w), end(w));
  return w;
}

template <typename T>
bool nxp(T &v) {
  return next_permutation(begin(v), end(v));
}

// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
  vector<vector<T>> ret;
  vector<T> v;
  auto dfs = [&](auto rc, int i) -> void {
    if (i == (int)a.size()) {
      ret.push_back(v);
      return;
    }
    for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
  };
  dfs(dfs, 0);
  return ret;
}

// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
  T res = I;
  for (; n; f(a = a * a), n >>= 1) {
    if (n & 1) f(res = res * a);
  }
  return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
  return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}

template <typename T>
T Rev(const T &v) {
  T res = v;
  reverse(begin(res), end(res));
  return res;
}

template <typename T>
vector<T> Transpose(const vector<T> &v) {
  using U = typename T::value_type;
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      res[j][i] = v[i][j];
    }
  }
  return res;
}

template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
  using U = typename T::value_type;
  int H = v.size(), W = v[0].size();
  vector res(W, T(H, U{}));
  for (int i = 0; i < H; i++) {
    for (int j = 0; j < W; j++) {
      if (clockwise) {
        res[W - 1 - j][i] = v[i][j];
      } else {
        res[j][H - 1 - i] = v[i][j];
      }
    }
  }
  return res;
}

}  // namespace Nyaan


// bit operation

namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan


// inout

namespace Nyaan {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}

istream &operator>>(istream &is, __int128_t &x) {
  string S;
  is >> S;
  x = 0;
  int flag = 0;
  for (auto &c : S) {
    if (c == '-') {
      flag = true;
      continue;
    }
    x *= 10;
    x += c - '0';
  }
  if (flag) x = -x;
  return is;
}

istream &operator>>(istream &is, __uint128_t &x) {
  string S;
  is >> S;
  x = 0;
  for (auto &c : S) {
    x *= 10;
    x += c - '0';
  }
  return is;
}

ostream &operator<<(ostream &os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
  if (x == 0) return os << 0;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan


// debug


#ifdef NyaanDebug
#define trc(...) (void(0))
#else
#define trc(...) (void(0))
#endif

#ifdef NyaanLocal
#define trc2(...) (void(0))
#else
#define trc2(...) (void(0))
#endif


// macro

#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)


namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }


//


// LazySegmentTree
template <typename T, typename E, typename F, typename G, typename H>
struct LazySegmentTree {
  int n, height;
  F f;
  G g;
  H h;
  T ti;
  E ei;
  vector<T> dat;
  vector<E> laz;
  LazySegmentTree(int _n, F _f, G _g, H _h, T _ti, E _ei)
      : f(_f), g(_g), h(_h), ti(_ti), ei(_ei) {
    init(_n);
  }
  LazySegmentTree(const vector<T> &v, F _f, G _g, H _h, T _ti, E _ei)
      : f(_f), g(_g), h(_h), ti(_ti), ei(_ei) {
    init((int)v.size());
    build(v);
  }
  void init(int _n) {
    n = 1;
    height = 0;
    while (n < _n) n <<= 1, height++;
    dat.assign(2 * n, ti);
    laz.assign(2 * n, ei);
  }
  void build(const vector<T> &v) {
    int _n = v.size();
    init(_n);
    for (int i = 0; i < _n; i++) dat[n + i] = v[i];
    for (int i = n - 1; i; i--)
      dat[i] = f(dat[(i << 1) | 0], dat[(i << 1) | 1]);
  }
  inline T reflect(int k) { return laz[k] == ei ? dat[k] : g(dat[k], laz[k]); }
  inline void eval(int k) {
    if (laz[k] == ei) return;
    laz[(k << 1) | 0] = h(laz[(k << 1) | 0], laz[k]);
    laz[(k << 1) | 1] = h(laz[(k << 1) | 1], laz[k]);
    dat[k] = reflect(k);
    laz[k] = ei;
  }
  inline void thrust(int k) {
    for (int i = height; i; i--) eval(k >> i);
  }
  inline void recalc(int k) {
    while (k >>= 1) dat[k] = f(reflect((k << 1) | 0), reflect((k << 1) | 1));
  }
  void update(int a, int b, E x) {
    if (a >= b) return;
    thrust(a += n);
    thrust(b += n - 1);
    for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
      if (l & 1) laz[l] = h(laz[l], x), l++;
      if (r & 1) --r, laz[r] = h(laz[r], x);
    }
    recalc(a);
    recalc(b);
  }
  void set_val(int a, T x) {
    thrust(a += n);
    dat[a] = x;
    laz[a] = ei;
    recalc(a);
  }
  T get_val(int a) {
    thrust(a += n);
    return reflect(a);
  }
  T query(int a, int b) {
    if (a >= b) return ti;
    thrust(a += n);
    thrust(b += n - 1);
    T vl = ti, vr = ti;
    for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
      if (l & 1) vl = f(vl, reflect(l++));
      if (r & 1) vr = f(reflect(--r), vr);
    }
    return f(vl, vr);
  }
};

using namespace Nyaan;

// https://ei1333.github.io/library/structure/bbst/persistent-red-black-tree.hpp
namespace ei1333 {

template <class T>
struct VectorPool {
  vector<T> pool;
  vector<T *> stock;
  int ptr;

  VectorPool() = default;

  VectorPool(int sz) : pool(sz), stock(sz) {}

  inline T *alloc() { return stock[--ptr]; }

  inline void free(T *t) { stock[ptr++] = t; }

  void clear() {
    ptr = (int)pool.size();
    for (int i = 0; i < (int)pool.size(); i++) stock[i] = &pool[i];
  }
};

/**
 * @brief Weight-Balanced-Tree(重み平衡木)
 */
template <typename Monoid, typename F>
struct WeightBalancedTree {
 public:
  struct Node {
    Node *l, *r;
    int cnt;
    Monoid key, sum;

    Node() {}

    Node(const Monoid &k) : key(k), sum(k), l(nullptr), r(nullptr), cnt(1) {}

    Node(Node *l, Node *r, const Monoid &k) : key(k), l(l), r(r) {}

    bool is_leaf() { return !l || !r; }
  };

 private:
  Node *update(Node *t) {
    t->cnt = count(t->l) + count(t->r) + t->is_leaf();
    t->sum = f(f(sum(t->l), t->key), sum(t->r));
    return t;
  }

  inline Node *alloc(Node *l, Node *r) {
    auto t = &(*pool.alloc() = Node(l, r, M1));
    return update(t);
  }

  Node *submerge(Node *l, Node *r) {
    if (count(l) > count(r) * 4) {
      l = clone(l);
      auto nl = clone(l->l);
      auto nr = submerge(l->r, r);
      if (count(nl) * 4 >= count(nr)) {
        l->r = nr;
        return update(l);
      }
      if (count(nr->l) * 3 <= count(nr->r) * 5) {
        l->r = nr->l;
        nr->l = l;
        update(l);
        return update(nr);
      }
      Node *t = clone(nr->l);
      l->r = nr->l->l;
      update(l);
      nr->l = nr->l->r;
      update(nr);
      t->l = l;
      t->r = nr;
      return update(t);
    }
    if (count(l) * 4 < count(r)) {
      r = clone(r);
      auto nl = submerge(l, r->l);
      auto nr = clone(r->r);
      if (count(nl) <= count(nr) * 4) {
        r->l = nl;
        return update(r);
      }
      if (count(nl->l) * 5 >= count(nl->r) * 3) {
        r->l = nl->r;
        nl->r = r;
        update(r);
        return update(nl);
      }
      Node *t = clone(nl->r);
      r->l = nl->r->r;
      update(r);
      nl->r = nl->r->l;
      update(nl);
      t->r = r;
      t->l = nl;
      return update(t);
    }
    return alloc(l, r);
  }

  Node *build(int l, int r, const vector<Monoid> &v) {
    if (l + 1 >= r) return alloc(v[l]);
    return merge(build(l, (l + r) >> 1, v), build((l + r) >> 1, r, v));
  }

  void dump(Node *r, typename vector<Monoid>::iterator &it) {
    if (r->is_leaf()) {
      *it++ = r->key;
      return;
    }
    dump(r->l, it);
    dump(r->r, it);
  }

  virtual Node *clone(Node *t) { return t; }

  Node *merge(Node *l) { return l; }

  Monoid query(Node *t, int a, int b, int l, int r) {
    if (r <= a || b <= l) return M1;
    if (a <= l && r <= b) return t->sum;
    return f(query(t->l, a, b, l, l + count(t->l)),
             query(t->r, a, b, r - count(t->r), r));
  }

 public:
  VectorPool<Node> pool;
  const F f;
  const Monoid M1;

  WeightBalancedTree(int sz, const F &f, const Monoid &M1)
      : pool(sz), M1(M1), f(f) {
    pool.clear();
  }

  inline Node *alloc(const Monoid &key) { return &(*pool.alloc() = Node(key)); }

  static inline int count(const Node *t) { return t ? t->cnt : 0; }

  inline const Monoid &sum(const Node *t) { return t ? t->sum : M1; }

  pair<Node *, Node *> split(Node *t, int k) {
    if (!t) return {nullptr, nullptr};
    if (k == 0) return {nullptr, t};
    if (k >= count(t)) return {t, nullptr};
    t = clone(t);
    Node *l = t->l, *r = t->r;
    pool.free(t);
    if (k < count(l)) {
      auto pp = split(l, k);
      return {pp.first, merge(pp.second, r)};
    }
    if (k > count(l)) {
      auto pp = split(r, k - count(l));
      return {merge(l, pp.first), pp.second};
    }
    return {l, r};
  }

  // (first の sum が k 以下) で切る
  pair<Node *, Node *> split_by_sum(Node *t, ll k) {
    if (!t) return {nullptr, nullptr};
    if (k == 0) return {nullptr, t};
    if (k >= sum(t).first) return {t, nullptr};
    if (t->is_leaf()) return {nullptr, t};
    t = clone(t);
    Node *l = t->l, *r = t->r;
    pool.free(t);
    if (k < sum(l).first) {
      auto pp = split_by_sum(l, k);
      return {pp.first, merge(pp.second, r)};
    }
    if (k > sum(l).first) {
      auto pp = split_by_sum(r, k - sum(l).first);
      return {merge(l, pp.first), pp.second};
    }
    return {l, r};
  }

  // 前 k 個の sum
  ll calc_sum(Node *t, ll k) {
    if (!t) return 0;
    if (k == 0) return 0;
    if (sum(t).first <= k) return sum(t).second;
    if (t->is_leaf()) {
      auto [num, val] = sum(t);
      return val / num * k;
    }
    auto [lnum, lsum] = sum(t->l);
    if (k < lnum) return calc_sum(t->l, k);
    if (k > lnum) return calc_sum(t->r, k - lnum) + lsum;
    return lsum;
  }

  tuple<Node *, Node *, Node *> split3(Node *t, int a, int b) {
    auto x = split(t, a);
    auto y = split(x.second, b - a);
    return make_tuple(x.first, y.first, y.second);
  }

  template <typename... Args>
  Node *merge(Node *l, Args... rest) {
    Node *r = merge(rest...);
    if (!l || !r) return l ? l : r;
    return submerge(l, r);
  }

  Node *build(const vector<Monoid> &v) { return build(0, (int)v.size(), v); }

  vector<Monoid> dump(Node *r) {
    vector<Monoid> v((size_t)count(r));
    auto it = begin(v);
    dump(r, it);
    return v;
  }

  string to_string(Node *r) {
    auto s = dump(r);
    string ret;
    for (int i = 0; i < s.size(); i++) {
      ret += std::to_string(s[i]);
      ret += ", ";
    }
    return ret;
  }

  void insert(Node *&t, int k, const Monoid &v) {
    auto x = split(t, k);
    t = merge(merge(x.first, alloc(v)), x.second);
  }

  Monoid erase(Node *&t, int k) {
    auto x = split(t, k);
    auto y = split(x.second, 1);
    auto v = y.first->c;
    pool.free(y.first);
    t = merge(x.first, y.second);
    return v;
  }

  Monoid query(Node *t, int a, int b) { return query(t, a, b, 0, count(t)); }

  void set_element(Node *&t, int k, const Monoid &x) {
    t = clone(t);
    if (t->is_leaf()) {
      t->key = t->sum = x;
      return;
    }
    if (k < count(t->l))
      set_element(t->l, k, x);
    else
      set_element(t->r, k - count(t->l), x);
    t = update(t);
  }

  void push_front(Node *&t, const Monoid &v) { t = merge(alloc(v), t); }

  void push_back(Node *&t, const Monoid &v) { t = merge(t, alloc(v)); }

  Monoid pop_front(Node *&t) {
    auto ret = split(t, 1);
    t = ret.second;
    return ret.first->key;
  }

  Monoid pop_back(Node *&t) {
    auto ret = split(t, count(t) - 1);
    t = ret.first;
    return ret.second->key;
  }
};

/**
 * @brief Persistent-Weight-Balanced-Tree(永続重み平衡木)
 */
template <typename Monoid, typename F, size_t FULL = 1000>
struct PersistentWeightBalancedTree : WeightBalancedTree<Monoid, F> {
  using WBT = WeightBalancedTree<Monoid, F>;
  using WBT::WeightBalancedTree;
  using Node = typename WBT::Node;

 private:
  Node *clone(Node *t) override { return &(*WBT::pool.alloc() = *t); }

 public:
  Node *rebuild(Node *r) {
    auto ret = WBT::dump(r);
    WBT::pool.clear();
    return WBT::build(ret);
  }

  bool almost_full() const { return this->pool.ptr < FULL; }
};

template <typename E, typename H>
struct DualSegmentTree {
  int sz, height;
  vector<E> lazy;
  const H h;
  const E ei;

  DualSegmentTree(int n, const H h, const E &ei) : h(h), ei(ei) {
    sz = 1;
    height = 0;
    while (sz < n) sz <<= 1, height++;
    lazy.assign(2 * sz, ei);
  }

  inline void propagate(int k) {
    if (lazy[k] != ei) {
      lazy[2 * k + 0] = h(lazy[2 * k + 0], lazy[k]);
      lazy[2 * k + 1] = h(lazy[2 * k + 1], lazy[k]);
      lazy[k] = ei;
    }
  }

  inline void thrust(int k) {
    for (int i = height; i > 0; i--) propagate(k >> i);
  }

  void update(int a, int b, const E &x) {
    thrust(a += sz);
    thrust(b += sz - 1);
    for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
      if (l & 1) lazy[l] = h(lazy[l], x), ++l;
      if (r & 1) --r, lazy[r] = h(lazy[r], x);
    }
  }

  E operator[](int k) {
    thrust(k += sz);
    return lazy[k];
  }
};

template <typename E, typename H>
DualSegmentTree<E, H> get_dual_segment_tree(int N, const H &h, const E &ei) {
  return {N, h, ei};
}

}  // namespace ei1333

void q() {
  inl(N, Q);
  // (要素の個数, 総和) の tuple
  auto ff = [&](pl a, pl b) -> pl { return a + b; };
  pl ti{0, 0};
  ei1333::PersistentWeightBalancedTree<pl, decltype(ff), TEN(6)> rbt(
      1.7 * TEN(7), ff, ti);

  using Node = typename decltype(rbt)::Node;
  using Ptr = Node *;

  using E = pair<ll, Ptr>;
  E ei{0, nullptr};

  // 先頭 k 個までで cut して先頭側だけを取り出す
  auto cut = [&](Ptr p, ll k) -> Ptr {
    auto [l, r] = rbt.split_by_sum(p, k);
    if (rbt.sum(l).first < k and rbt.sum(r).first > 0) {
      ll lack = k - rbt.sum(l).first;
      auto m = rbt.query(r, 0, 1);
      ll num = m.first;
      ll val = m.second / m.first;
      assert(0 < lack and lack < num);
      rbt.push_back(l, mkp(lack, lack * val));
    }
    return l;
  };
  //
  auto h = [&](E a, E b) -> E {
    if (b.fi == 0) return mkp(a.fi, rbt.merge(a.se, b.se));
    ll s = rbt.sum(a.se).first;
    if (s <= b.fi) return mkp(a.fi + b.fi - s, b.se);
    auto l = cut(a.se, s - b.fi);
    return mkp(a.fi, rbt.merge(l, b.se));
  };

  ei1333::DualSegmentTree seg(N, h, ei);

  trc2(sizeof(Node));

  rep(i, Q) {
    ini(cmd);
    trc(cmd);
    E e{0, nullptr};
    if (cmd == 1) {
      inl(l, r, x, y);
      --l;
      rbt.push_back(e.se, {x, x * y});
      seg.update(l, r, e);
    } else if (cmd == 2) {
      inl(l, r, x);
      --l;
      e.fi = x;
      seg.update(l, r, e);
    } else {
      inl(k, p, q);
      --k, --p;
      auto [val, root] = seg[k];
      ll ans = rbt.calc_sum(root, q) - rbt.calc_sum(root, p);
      out(ans);
    }

    if (i % TEN(3) == 0) {
      trc2(i, rbt.pool.ptr);
    }
  }
  trc2("OK");
}

void Nyaan::solve() {
  int t = 1;
  // in(t);
  while (t--) q();
}