/**
 * date   : 2024-11-23 14:58:59
 * 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 <tr2/dynamic_bitset>
#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>
  constexpr 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;
  if(v.empty()) return {};
  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 __builtin_popcountll(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))
#endif
#ifndef NyaanDebug
#define trc(...) (void(0))
#endif

#ifndef NyaanLocal
#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(); }


//



using namespace std;






using namespace std;

namespace internal {
template <typename T>
using is_broadly_integral =
    typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> ||
                               is_same_v<T, __uint128_t>,
                           true_type, false_type>::type;

template <typename T>
using is_broadly_signed =
    typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>,
                           true_type, false_type>::type;

template <typename T>
using is_broadly_unsigned =
    typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>,
                           true_type, false_type>::type;

#define ENABLE_VALUE(x) \
  template <typename T> \
  constexpr bool x##_v = x<T>::value;

ENABLE_VALUE(is_broadly_integral);
ENABLE_VALUE(is_broadly_signed);
ENABLE_VALUE(is_broadly_unsigned);
#undef ENABLE_VALUE

#define ENABLE_HAS_TYPE(var)                                   \
  template <class, class = void>                               \
  struct has_##var : false_type {};                            \
  template <class T>                                           \
  struct has_##var<T, void_t<typename T::var>> : true_type {}; \
  template <class T>                                           \
  constexpr auto has_##var##_v = has_##var<T>::value;

#define ENABLE_HAS_VAR(var)                                     \
  template <class, class = void>                                \
  struct has_##var : false_type {};                             \
  template <class T>                                            \
  struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \
  template <class T>                                            \
  constexpr auto has_##var##_v = has_##var<T>::value;

}  // namespace internal


ENABLE_HAS_VAR(lazy);
ENABLE_HAS_VAR(shift);

template <typename Node, typename I, typename T, typename E, T (*f)(T, T),
          T (*g)(T, E), E (*h)(E, E), T (*ti)(), E (*ei)()>
struct RBSTSegmentTreeBase {
 protected:
  using Ptr = Node *;
  template <typename... Args>
  static Ptr _my_new(Args... args) {
    return new Node(args...);
  }
  static void _my_del(Ptr t) { delete t; }

  static int _count(const Ptr t) { return t ? t->cnt : 0; }

  static T _sum(const Ptr &t) { return t ? t->sum : ti(); }

  static uint64_t _rng() {
    static uint64_t x_ = 88172645463325252ULL;
    return x_ ^= x_ << 7, x_ ^= x_ >> 9, x_ & 0xFFFFFFFFull;
  }

  static Ptr _merge(Ptr l, Ptr r) {
    if (!l || !r) return l ? l : r;
    if (int((_rng() * (l->cnt + r->cnt)) >> 32) < l->cnt) {
      _push(l);
      l->r = _merge(l->r, r);
      return _update(l);
    } else {
      _push(r);
      r->l = _merge(l, r->l);
      return _update(r);
    }
  }

  static Ptr _build(int l, int r, const vector<pair<I, T>> &dat) {
    if (l == r) return nullptr;
    if (l + 1 == r) return _my_new(dat[l].first, dat[l].second);
    int m = (l + r) / 2;
    return _merge(_build(l, m, dat), _build(m, r, dat));
  };

  static void _push([[maybe_unused]] Ptr t) {
    if constexpr (has_lazy_v<Node>) {
      if (!t) return;
      if (t->lazy != ei()) {
        if (t->l) _propagate(t->l, t->lazy);
        if (t->r) _propagate(t->r, t->lazy);
        t->lazy = ei();
      }
    }
    if constexpr (has_shift_v<Node>) {
      if (!t) return;
      if (t->shift != I{}) {
        if (t->l) _shift(t->l, t->shift);
        if (t->r) _shift(t->r, t->shift);
        t->shift = I{};
      }
    }
  }
  static void _propagate([[maybe_unused]] Ptr t, [[maybe_unused]] const E &x) {
    if constexpr (has_lazy_v<Node>) {
      if (!t) return;
      t->lazy = h(t->lazy, x);
      t->val = g(t->val, x);
      t->sum = g(t->sum, x);
    }
  }
  static void _shift([[maybe_unused]] Ptr t, [[maybe_unused]] const I &sh) {
    if constexpr (has_shift_v<Node>) {
      if (!t) return;
      t->key += sh, t->shift += sh;
    }
  }

  static Ptr _update(Ptr t) {
    if (!t) return t;
    t->cnt = 1;
    t->sum = t->val;
    if (t->l) t->cnt += t->l->cnt, t->sum = f(t->l->sum, t->sum);
    if (t->r) t->cnt += t->r->cnt, t->sum = f(t->sum, t->r->sum);
    return t;
  }

  // key が k であるノードを探す, なければ nullptr
  static Ptr _find(Ptr t, I k) {
    while (t) {
      _push(t);
      if (k == t->key) return t;
      t = k < t->key ? t->l : t->r;
    }
    return nullptr;
  }

  static void _erase(Ptr &t, I k) {
    if (!t) return;
    _push(t);
    if (k == t->key) {
      Ptr tl = t->l, tr = t->r;
      _my_del(t);
      t = _merge(tl, tr);
    } else if (k < t->key) {
      _erase(t->l, k);
      _update(t);
    } else {
      _erase(t->r, k);
      _update(t);
    }
  }

  // [k 未満, k 以上]
  static pair<Ptr, Ptr> _split_by_key(Ptr t, I k) {
    if (!t) return {nullptr, nullptr};
    _push(t);
    if (k == t->key) {
      Ptr tl = t->l;
      t->l = nullptr;
      return {tl, _update(t)};
    } else if (k < t->key) {
      auto s = _split_by_key(t->l, k);
      t->l = s.second;
      return {s.first, _update(t)};
    } else {
      auto s = _split_by_key(t->r, k);
      t->r = s.first;
      return {_update(t), s.second};
    }
  }

  // [k 未満, k, k 超過]
  static array<Ptr, 3> _split_by_key3(Ptr t, I k) {
    if (!t) return {{nullptr, nullptr, nullptr}};
    _push(t);
    if (k == t->key) {
      Ptr tl = t->l, tr = t->r;
      t->l = t->r = nullptr;
      return {{tl, _update(t), tr}};
    } else if (k < t->key) {
      auto s = _split_by_key3(t->l, k);
      t->l = s[2];
      return {{s[0], s[1], _update(t)}};
    } else {
      auto s = _split_by_key3(t->r, k);
      t->r = s[0];
      return {{_update(t), s[1], s[2]}};
    }
  }

  // (-inf, i] の prod について check(prod) の (true / false) で切る
  template <typename C>
  static pair<Ptr, Ptr> _split_max_right(Ptr t, const C &check, T prod = ti()) {
    assert(check(prod));
    if (!t) return {nullptr, nullptr};
    _push(t);
    T p1 = f(prod, _sum(t->l));
    if (check(p1)) {
      prod = p1;
    } else {
      auto s = _split_max_right(t->l, check, prod);
      t->l = s.second;
      return {s.first, _update(t)};
    }
    prod = f(prod, t->val);
    if (!check(prod)) {
      Ptr tl = t->l;
      t->l = nullptr;
      return {tl, _update(t)};
    }
    p1 = f(prod, _sum(t->r));
    if (check(p1)) {
      return {t, nullptr};
    } else {
      auto s = _split_max_right(t->r, check, prod);
      t->r = s.first;
      return {_update(t), s.second};
    }
  }

  // [i, inf) の prod について check(prod) の (false / true) で切る
  template <typename C>
  static pair<Ptr, Ptr> _split_min_left(Ptr t, const C &check, T prod = ti()) {
    assert(check(prod));
    if (!t) return {nullptr, nullptr};
    _push(t);
    T p1 = f(_sum(t->r), prod);
    if (check(p1)) {
      prod = p1;
    } else {
      auto s = _split_min_left(t->r, check, prod);
      t->r = s.first;
      return {_update(t), s.second};
    }
    prod = f(t->val, prod);
    if (!check(prod)) {
      Ptr tr = t->r;
      t->r = nullptr;
      return {_update(t), tr};
    }
    p1 = f(_sum(t->l), prod);
    if (check(p1)) {
      return {nullptr, t};
    } else {
      auto s = _split_min_left(t->l, check, prod);
      t->l = s.second;
      return {s.first, _update(t)};
    }
  }

  // [l, inf) である地点に apply
  static void _apply_left(Ptr t, I l, const E &e) {
    if (!t) return;
    _push(t);
    if (t->key < l) {
      _apply_left(t->r, l, e);
    } else if (t->key == l) {
      t->val = g(t->val, e);
      _propagate(t->r, e);
    } else {
      _apply_left(t->l, l, e);
      t->val = g(t->val, e);
      _propagate(t->r, e);
    }
    _update(t);
  }

  // [-inf, r) である地点に apply
  static void _apply_right(Ptr t, I r, const E &e) {
    if (!t) return;
    _push(t);
    if (t->key < r) {
      _propagate(t->l, e);
      t->val = g(t->val, e);
      _apply_right(t->r, r, e);
    } else if (t->key == r) {
      _propagate(t->l, e);
    } else {
      _apply_right(t->l, r, e);
    }
    _update(t);
  }

  // [l, r) に apply
  static void _apply(Ptr t, I l, I r, const E &e) {
    if (!t) return;
    _push(t);
    if (t->key < l) {
      _apply(t->r, l, r, e);
    } else if (t->key == l) {
      t->val = g(t->val, e);
      _apply_right(t->r, r, e);
    } else if (t->key < r) {
      _apply_left(t->l, l, e);
      t->val = g(t->val, e);
      _apply_right(t->r, r, e);
    } else if (t->key == r) {
      _apply_left(t->l, l, e);
    } else {
      _apply(t->l, l, r, e);
    }
    _update(t);
  }

  // l 以上
  static T _fold_left(Ptr t, I l) {
    if (!t) return ti();
    _push(t);
    if (t->key < l) {
      return _fold_left(t->r, l);
    } else if (t->key == l) {
      return f(t->val, _fold_left(t->r, l));
    } else {
      T tl = _fold_left(t->l, l);
      return f(f(tl, t->val), _sum(t->r));
    }
  }

  // r 未満
  static T _fold_right(Ptr t, I r) {
    if (!t) return ti();
    _push(t);
    if (t->key < r) {
      T tr = _fold_right(t->r, r);
      return f(f(_sum(t->l), t->val), tr);
    } else if (t->key == r) {
      return _sum(t->l);
    } else {
      return _fold_right(t->l, r);
    }
  }

  static T _fold(Ptr t, I l, I r) {
    if (!t) return ti();
    _push(t);
    if (t->key < l) {
      return _fold(t->r, l, r);
    } else if (t->key == l) {
      return f(t->val, _fold_right(t->r, r));
    } else if (t->key < r) {
      T tl = _fold_left(t->l, l);
      T tr = _fold_right(t->r, r);
      return f(f(tl, t->val), tr);
    } else if (t->key == r) {
      return _fold_left(t->l, l);
    } else {
      return _fold(t->l, l, r);
    }
  }

  // t を根とする木の上で最小の key は？ (t が空の場合は failed)
  static pair<I, T> _get_min_keyval(Ptr t, const I &failed) {
    if (!t) return {failed, ti()};
    while (t->l) _push(t), t = t->l;
    return {t->key, t->val};
  }

  // t を根とする木の上で最小の key は？ (t が空の場合は failed)
  static pair<I, T> _get_max_keyval(Ptr t, const I &failed) {
    if (!t) return {failed, ti()};
    while (t->r) _push(t), t = t->r;
    return {t->key, t->val};
  }

  // t を根とする木のうち、[0, i の区間 fold が true になる最大の i は何か？
  // exclusive かつ (空 または[0,右]が真の場合) の場合は failed(inf)
  // inclusive かつ (空 または[0,0] が偽の場合) の場合は failed
  template <typename C, bool exclusive>
  static I _max_right(Ptr t, C check, const I &failed) {
    if (!t) return failed;
    _push(t);
    Ptr now = t;
    T prod_now = ti();
    [[maybe_unused]] I prev = failed;
    while (true) {
      if (now->l != nullptr) {
        _push(now->l);
        auto pl = f(prod_now, now->l->sum);
        if (check(pl)) {
          prod_now = pl;
        } else {
          now = now->l;
          continue;
        }
      }
      auto pl = f(prod_now, now->val);
      if (!check(pl)) {
        if constexpr (exclusive) {
          return now->key;
        } else {
          return now->l ? _get_max_keyval(now->l, failed).first : prev;
        }
      }
      prod_now = pl;
      if (now->r == nullptr) {
        if constexpr (exclusive) {
          return failed;
        } else {
          return now->key;
        }
      }
      _push(now->r);
      if constexpr (!exclusive) prev = now->key;
      now = now->r;
    }
  }

  // t を根とする木のうち、i, inf) の区間 fold が true になる最小の i は何か？
  // inclusive かつ (空 または 存在しない) 場合は failed
  // exlucisve かつ (空 または [左, inf) が真) の場合は failed
  template <typename C, bool inclusive>
  static I _min_left(Ptr t, C check, const I &failed) {
    if (!t) return failed;
    _push(t);
    Ptr now = t;
    T prod_now = ti();
    [[maybe_unused]] I prev = failed;
    while (true) {
      if (now->r != nullptr) {
        _push(now->r);
        auto pr = f(now->r->sum, prod_now);
        if (check(pr)) {
          prod_now = pr;
        } else {
          now = now->r;
          continue;
        }
      }
      auto pr = f(now->val, prod_now);
      if (!check(pr)) {
        if constexpr (inclusive) {
          return now->r ? _get_min_keyval(now->r, failed).first : prev;
        } else {
          return now->key;
        }
      }
      prod_now = pr;
      if (now->l == nullptr) {
        if constexpr (inclusive) {
          return now->key;
        } else {
          return failed;
        }
      }
      _push(now->l);
      if constexpr (inclusive) prev = now->key;
      now = now->l;
    }
  }

  static void _clear(Ptr t) {
    if (!t) return;
    if (t->l) _clear(t->l);
    if (t->r) _clear(t->r);
    _my_del(t);
  }

  static Ptr _deepcopy(Ptr t) {
    if (!t) return nullptr;
    Ptr u = _my_new(*t);
    if (u->l) u->l = _deepcopy(u->l);
    if (u->r) u->r = _deepcopy(u->r);
    return u;
  }

  static void _dump(Ptr t) {
    if (!t) return;
    _push(t);
    _dump(t->l);
    cerr << "## key = " << t->key << ",";
    cerr << "\tval = " << t->val << ", ";
    cerr << "\tsum = " << t->sum << ", ";
    cerr << "\tchild = ";
    cerr << "( ";
    if (t->l) cerr << t->l->key;
    if (!t->l) cerr << "nil";
    cerr << ", ";
    if (t->r) cerr << t->r->key;
    if (!t->r) cerr << "nil";
    cerr << " )" << endl;
    _dump(t->r);
  }

  static void _make_array(Ptr t, vector<pair<I, T>> &v) {
    if (!t) return;
    _push(t);
    if (t->l) _make_array(t->l, v);
    v.emplace_back(t->key, t->val);
    if (t->r) _make_array(t->r, v);
  }

 public:
  Ptr root;

  RBSTSegmentTreeBase() : root(nullptr) {}
  RBSTSegmentTreeBase(Ptr t) : root(t) {}
  RBSTSegmentTreeBase(const vector<T> xs, const vector<I> &vals = {}) {
    if (!vals.empty()) assert(xs.size() == vals.size());
    int n = xs.size();
    vector<pair<I, T>> dat(n);
    for (int i = 0; i < n; i++) dat[i] = {vals.empty() ? i : vals[i], xs[i]};
    root = _build(0, n, dat);
  }
  RBSTSegmentTreeBase(RBSTSegmentTreeBase &&rhs) noexcept { root = rhs.root; }
  RBSTSegmentTreeBase(const RBSTSegmentTreeBase &rhs) { root = rhs.root; }
  ~RBSTSegmentTreeBase() = default;

  using RBST = RBSTSegmentTreeBase;
  RBST &operator=(RBST &&rhs) noexcept {
    root = rhs.root;
    return *this;
  }
  RBST &operator=(const RBST &rhs) {
    root = rhs.root;
    return *this;
  }
  RBST deepcopy() { return _deepcopy(root); }

  friend void swap(RBST &lhs, RBST &rhs) { swap(lhs.root, rhs.root); }
  void swap(RBST &rhs) { swap(root, rhs.root); }

  // destructive ordered _merge (max(lhs) < min(rhs))
  friend RBST ordered_merge(RBST &lhs, RBST &rhs) {
    assert(lhs.get_max_key() < rhs.get_min_key());
    return RBST{_merge(lhs.root, rhs.root)};
  }

  // 1 点 値の書き換え
  void set_val(I i, T x) {
    auto s = _split_by_key3(root, i);
    if (s[1] == nullptr) {
      s[1] = _my_new(i, x);
    } else {
      s[1]->val = x;
    }
    root = _merge(_merge(s[0], _update(s[1])), s[2]);
  }

  // すでに要素が存在するときに値を set する。おそらく少し早い
  void set_val_fast(I i, T x) {
    static vector<Ptr> ps;
    ps.clear();
    Ptr t = root;
    while (t) {
      _push(t);
      ps.push_back(t);
      if (i == t->key) break;
      t = i < t->key ? t->l : t->r;
    }
    if (!t) {
      set_val(i, x);
      return;
    }
    t->val = x;
    for (int j = ps.size() - 1; j >= 0; j--) _update(ps[j]);
  }

  // 1 点取得
  T get_val(I i) {
    Ptr p = _find(root, i);
    return p ? p->val : ti();
  }
  bool exist(I i) {
    Ptr p = _find(root, i);
    return p != nullptr;
  }

  // 1 点 値の書き換え
  // func の返り値は void !!!!!!(参照された値を直接更新する)
  void apply_val(I i, const function<void(T &)> &func) {
    auto s = _split_by_key3(root, i);
    if (s[1] == nullptr) s[1] = _my_new(i);
    func(s[1]->val);
    root = _merge(_merge(s[0], _update(s[1])), s[2]);
  }
  // 1 点 値の書き換え 値が既に存在するときに早い
  // func の返り値は void !!!!!!(参照された値を直接更新する)
  void apply_val_fast(I i, const function<void(T &)> &func) {
    static vector<Ptr> ps;
    ps.clear();
    Ptr t = root;
    while (t) {
      _push(t);
      ps.push_back(t);
      if (i == t->key) break;
      t = i < t->key ? t->l : t->r;
    }
    if (!t) {
      apply_val(i, func);
      return;
    }
    func(t->val);
    for (int j = ps.size() - 1; j >= 0; j--) _update(ps[j]);
  }

  // 頂点の削除
  virtual void erase(I i) { _erase(root, i); }

  // 範囲作用
  void apply(I l, I r, const E &e) {
    if (l >= r) return;
    _apply(root, l, r, e);
  }
  void apply_all(const E &e) { _propagate(root, e); }

  // 範囲取得
  T fold(I l, I r) {
    if (l >= r) return ti();
    return _fold(root, l, r);
  }
  T fold_all() { return _sum(root); }

  void shift(const I &sh) { _shift(root, sh); }

  // key 最小を取得
  I get_min_key(I failed = {}) { return _get_min_keyval(root, failed).first; }
  // key 最大を取得
  I get_max_key(I failed = {}) { return _get_max_keyval(root, failed).first; }
  // (key, val) 最小を取得
  pair<I, T> get_min_keyval(I failed = {}) {
    return _get_min_keyval(root, failed);
  }
  // (key, val) 最大を取得
  pair<I, T> get_max_keyval(I failed = {}) {
    return _get_max_keyval(root, failed);
  }
  // (key, val) 最小を pop
  pair<I, T> pop_min_keyval(I failed = {}) {
    assert(root != nullptr);
    auto kv = _get_min_keyval(root, failed);
    erase(kv.first);
    return kv;
  }
  // (key, val) 最大を取得
  pair<I, T> pop_max_keyval(I failed = {}) {
    assert(root != nullptr);
    auto kv = _get_max_keyval(root, failed);
    erase(kv.first);
    return kv;
  }

  // n 未満の i のうち、[i, n) の区間 fold が true になる最小の i は何か？
  // (存在しない場合は failed を返す)
  template <typename C>
  I min_left(I n, C check, I failed) {
    assert(check(ti()) == true);
    auto [x, y] = _split_by_key(root, n);
    I res = _min_left<C, true>(x, check, failed);
    root = _merge(x, y);
    return res;
  }

  // n 未満の i のうち、(i, n) の区間 fold が true になる最小の i は何か？
  // (空だったり (左端, n) が 真の場合は minus_infty を返す)
  template <typename C>
  I min_left_exclusive(I n, C check, I minus_infty) {
    assert(check(ti()) == true);
    auto [x, y] = _split_by_key(root, n);
    I res = _min_left<C, false>(x, check, minus_infty);
    root = _merge(x, y);
    return res;
  }

  // n 以上の i のうち、[n, i) の区間 fold が true になる最大の i は何か？
  // (空だったり [n, 右端] が true の場合は infty を返す)
  template <typename C>
  I max_right(I n, C check, I infty) {
    assert(check(ti()) == true);
    auto [x, y] = _split_by_key(root, n);
    I res = _max_right<C, true>(y, check, infty);
    root = _merge(x, y);
    return res;
  }

  // n 以上の i のうち、[n, i] の区間 fold が true になる最大の i は何か？
  // (存在しない場合は failed を返す)
  template <typename C>
  I max_right_inclusive(I n, C check, I failed) {
    assert(check(ti()) == true);
    auto [x, y] = _split_by_key(root, n);
    I res = _max_right<C, false>(y, check, failed);
    root = _merge(x, y);
    return res;
  }

  // (key 未満, key 以上) で分割
  // 呼び出し後のオブジェクトは空のセグ木になる
  pair<RBST, RBST> split_by_key(const I &key) {
    auto [x, y] = _split_by_key(root, key);
    root = nullptr;
    return make_pair(RBST{x}, RBST{y});
  }
  // [i, inf) の区間積が (false, true) になる境界で分割
  // 呼び出し後のオブジェクトは空のセグ木になる
  template <typename C>
  pair<RBST, RBST> split_min_left(const C &check) {
    assert(check(ti()) == true);
    auto [x, y] = _split_min_left(root, check);
    root = nullptr;
    return make_pair(RBST{x}, RBST{y});
  }
  // (-inf, i] の区間積が (true, false) になる境界で分割
  // 呼び出し後のオブジェクトは空のセグ木になる
  template <typename C>
  pair<RBST, RBST> split_max_right(const C &check) {
    assert(check(ti()) == true);
    auto [x, y] = _split_max_right(root, check);
    root = nullptr;
    return make_pair(RBST{x}, RBST{y});
  }

  void clear() { _clear(root), root = nullptr; }
  int size() { return _count(root); }
  bool empty() { return !root; }
  void dump() {
    cerr << "***** dump start *****" << endl;
    _dump(root);
    cerr << "****** dump end ******" << endl;
  }

  // 列を配列に変換して返す
  vector<pair<I, T>> make_array() {
    vector<pair<I, T>> res;
    _make_array(root, res);
    return res;
  }
};

namespace RBSTSegmentTreeImpl {
bool _ei() { return false; }

template <typename I, typename T, typename E, T (*f)(T, T), T (*g)(T, E),
          E (*h)(E, E), T (*ti)(), E (*ei)()>
struct ShiftableLazySegNode {
  ShiftableLazySegNode *l, *r;
  I key, shift;
  T val, sum;
  E lazy;
  int cnt;
  ShiftableLazySegNode(const I &i, const T &t = ti())
      : l(), r(), key(i), shift(I{}), val(t), sum(t), lazy(ei()), cnt(1) {}
};
template <typename I, typename T, typename E, T (*f)(T, T), T (*g)(T, E),
          E (*h)(E, E), T (*ti)(), E (*ei)()>
using RBSTShiftableLazySegmentTree =
    RBSTSegmentTreeBase<ShiftableLazySegNode<I, T, E, f, g, h, ti, ei>, I, T, E,
                        f, g, h, ti, ei>;

template <typename I, typename T, typename E, T (*f)(T, T), T (*g)(T, E),
          E (*h)(E, E), T (*ti)(), E (*ei)()>
struct LazySegNode {
  LazySegNode *l, *r;
  I key;
  T val, sum;
  E lazy;
  int cnt;
  LazySegNode(const I &i, const T &t = ti())
      : l(), r(), key(i), val(t), sum(t), lazy(ei()), cnt(1) {}
};
template <typename I, typename T, typename E, T (*f)(T, T), T (*g)(T, E),
          E (*h)(E, E), T (*ti)(), E (*ei)()>
using RBSTLazySegmentTree =
    RBSTSegmentTreeBase<LazySegNode<I, T, E, f, g, h, ti, ei>, I, T, E, f, g, h,
                        ti, ei>;

template <typename I, typename T, T (*f)(T, T), T (*ti)()>
struct SegNode {
  SegNode *l, *r;
  I key;
  T val, sum;
  int cnt;
  SegNode(const I &i, const T &t = ti())
      : l(), r(), key(i), val(t), sum(t), cnt(1) {}
};
template <typename I, typename T, T (*f)(T, T), T (*ti)()>
using RBSTSegmentTree = RBSTSegmentTreeBase<SegNode<I, T, f, ti>, I, T, bool, f,
                                            nullptr, nullptr, ti, _ei>;

}  // namespace RBSTSegmentTreeImpl

using RBSTSegmentTreeImpl::RBSTLazySegmentTree;
using RBSTSegmentTreeImpl::RBSTSegmentTree;
using RBSTSegmentTreeImpl::RBSTShiftableLazySegmentTree;

/**
 * @brief RBST-based Dynamic Lazy Segment Tree
 */


template <typename T, typename E, T (*f)(T, T), T (*g)(T, E), E (*h)(E, E),
          T (*ti)(), E (*ei)()>
struct Sequence : RBSTShiftableLazySegmentTree<int, T, E, f, g, h, ti, ei> {
  using Base = RBSTShiftableLazySegmentTree<int, T, E, f, g, h, ti, ei>;
  using Base::_clear;
  using Base::_count;
  using Base::_make_array;
  using Base::_merge;
  using Base::_my_del;
  using Base::_my_new;
  using Base::_shift;
  using Base::_split_by_key;
  using Base::_split_by_key3;

  Sequence() : Base() {}
  Sequence(const vector<T>& v) : Base(v) {}
  Sequence(int n) : Base(vector<T>(n, ti())) {}

  void insert(int i, const T& x) {
    auto [l, r] = _split_by_key(this->root, i);
    _shift(r, 1);
    this->root = _merge(_merge(l, _my_new(i, x)), r);
  }
  void push_back(const T& x) { insert(_count(this->root), x); }

  // 列のマージ　破壊的
  void append(Sequence& r) {
    _shift(r.root, _count(this->root));
    this->root = _merge(this->root, r.root);
    r.root = nullptr;
  }
  void append(const vector<T>& r) {
    Sequence s{r};
    append(s);
  }

  // 元の seq は空になる
  pair<Sequence, Sequence> split(int i) {
    auto s = _split_by_key(this->root, i);
    _shift(s.second, -i);
    this->root = nullptr;
    Sequence L, R;
    L.root = s.first, R.root = s.second;
    return make_pair(L, R);
  }

  void erase(int i) override {
    auto s = _split_by_key3(this->root, i);
    _my_del(s[1]), _shift(s[2], -1);
    this->root = _merge(s[0], s[2]);
  }
  void pop_back() { erase(_count(this->root) - 1); }

  void erase(int l, int r) {
    if (l >= r) return;
    auto s = _split_by_key3(this->root, l);
    auto [t, u] = _split_by_key(s[2], r);
    _my_del(s[1]), _clear(t), _shift(u, l - r);
    this->root = _merge(s[0], u);
  }

  vector<T> get_vector() {
    vector<pair<int, T>> buf;
    _make_array(this->root, buf);
    vector<T> res;
    for (auto& p : buf) res.push_back(p.second);
    return res;
  }

  friend ostream& operator<<(ostream& os, Sequence& s) {
    vector<pair<int, T>> p = s.make_array();
    for (int i = 0; i < (int)p.size(); i++) {
      os << (i ? " " : "") << p[i].second;
    }
    os << "\n";
    return os;
  }
};


using namespace Nyaan;

struct Data {
  char c;
  ll x;
  friend ostream& operator<<(ostream& os, Data& d) {
    return os << "(" << d.c << "," << d.x << ")";
  }
};
Data f(Data l, Data r) { return Data{l.c, l.x + r.x}; }
Data g(Data l, ll r) { return Data{l.c, l.x * r}; }
ll h(ll l, ll r) { return l * r; }
Data ti() { return {'?', 0}; }
ll ei() { return 1; }
using Seq = Sequence<Data, ll, f, g, h, ti, ei>;

void q() {
  inl(N, Q);
  ins(S);

  Seq seq;
  rep(i, N) seq.push_back(Data{S[i], 1});

  // [0, r) [r, inf) で cut する
  auto f = [&](ll r) -> pair<Seq, Seq> {
    if (r == 0) return {Seq{}, seq};
    int i = seq.max_right(-inf, [&](Data d) { return d.x < r; }, inf);
    auto [L, R] = seq.split(i);
    ll lsum = L.fold_all().x;
    if (lsum != r and !R.empty()) {
      Data d = R.get_val(0);
      R.erase(0);
      assert(r - lsum <= d.x);
      L.push_back(Data{d.c, r - lsum});
      d.x -= r - lsum;
      if (d.x) R.insert(0, d);
    }
    return make_pair(L, R);
  };

  while (Q--) {
    ini(cmd);
    if (cmd == 1) {
      inl(l, r);
      --l;
      auto [LM, R] = f(r);
      seq = LM;
      auto [L, M] = f(l);
      M.apply_all(2);
      L.append(M);
      L.append(R);
      seq = L;
      auto [s, yojo] = f(2 * TEN(18));
      seq = s;
    } else {
      inl(i);
      --i;
      auto [L, R] = f(i);
      out(R.get_val(0).c);
      L.append(R);
      seq = L;
    }

    //cerr << seq;
  }
}

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