Problem p02567 (C++)

Buggy submission (status: Runtime Error):
/*
#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/multiprecision/cpp_int.hpp>

#include <boost/rational.hpp>
*/
// #include <atcoder/all>
#include <bits/stdc++.h>
using namespace std;
// using namespace atcoder;
#define _GLIBCXX_DEBUG
#define rep(i, t) for (ll i = (ll)(0); i < (ll)(t); i++)
#define rep2(i, s, t) for (ll i = (ll)(s); i < (ll)(t); i++)
#define rep3(i, t) for (ll i = (ll)(1); i <= (ll)(t); i++)
#define rep4(i, s, t) for (ll i = (ll)(s); i <= (ll)(t); i++)
#define repr(i, t) for (ll i = (t - 1); i >= (0); i--)
#define repr2(i, s, t) for (ll i = (t - 1); i >= (s); i--)
#define repr3(i, t) for (ll i = (t); i >= (1); i--)
#define repr4(i, s, t) for (ll i = (t); i >= (s); i--)
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using uint = unsigned;
using pcc = pair<char, char>;
using pll = pair<ll, ll>;
using pii = pair<int, int>;
using pdd = pair<double, double>;
using tuplis = array<ll, 3>;
template <class T> using pq = priority_queue<T, vector<T>, greater<T>>;
inline const ll LINF = 1e18;
inline const ll MINF = 1e15;
inline const int INF = 1e9 + 1e5;
inline const int mod = 1000000007;
// inline const int mod=998244353;

inline const ld DINF = numeric_limits<ld>::infinity();
inline const ld EPS = 1e-9;
inline const ld PI = acos(-1);
// const ll dx[] ={0,1,0,-1,1,-1,1,-1};
// const ll dy[] ={1,0,-1,0,1,1,-1,-1};
inline const bool ingrid(const int i, const int j, const int H, const int W) {
  return i >= 0 && i < H && j >= 0 && j < W;
}
inline const ll dx[] = {0, 1, 0, -1};
inline const ll dy[] = {1, 0, -1, 0};
inline const bool is_low(char c) { return ('a' <= c) && (c <= 'z'); }
inline const bool is_upp(char c) { return ('A' <= c) && (c <= 'Z'); }
#define each1(i, a) for (auto &&i : a)
#define each2(x, y, a) for (auto &&[x, y] : a)
#define each3(x, y, z, a) for (auto &&[x, y, z] : a)
#define rrep(n) for (ll i = (n); i--;)
#define stlen(s) ll s.size() - 1
#define all(v) begin(v), end(v)
#define range(v, a) begin(v), begin(v) + a
#define range2(v, a, b) begin(v) + a, begin(v) + b
#define range3(v, a) begin(v) + 1, begin(v) + a + 1
#define range4(v, a, b) begin(v) + a + 1, begin(v) + b + 1
#define allr(v) rbegin(v), v.rend(v)
#define ranger(v, a) rbegin(v), rbegin(v) + a
#define ranger2(v, a, b) rbegin(v) + a, rbegin(v) + b
#define ranger3(v, a) rbegin(v) + 1, rbegin(v) + a + 1
#define ranger4(v, a, b) rbegin(v) + a + 1, rbegin(v) + b + 1
#define cout(n) cout << std::fixed << std::setprecision(n)
// #define sum(...) accumulate(all(__VA_ARGS__),0LL)
#define dsum(...) accumulate(all(__VA_ARGS__), 0.0L)
#define elif else if
#define unless(a) if (!(a))
#define mp make_pair
#define mt make_tuple
#define INT(...)                                                               \
  int __VA_ARGS__;                                                             \
  in(__VA_ARGS__)
#define LL(...)                                                                \
  ll __VA_ARGS__;                                                              \
  in(__VA_ARGS__)
#define ULL(...)                                                               \
  ull __VA_ARGS__;                                                             \
  in(__VA_ARGS__)
#define STR(...)                                                               \
  string __VA_ARGS__;                                                          \
  in(__VA_ARGS__)
#define CHR(...)                                                               \
  char __VA_ARGS__;                                                            \
  in(__VA_ARGS__)
#define DBL(...)                                                               \
  double __VA_ARGS__;                                                          \
  in(__VA_ARGS__)
#define LD(...)                                                                \
  ld __VA_ARGS__;                                                              \
  in(__VA_ARGS__)
#define Sort(a) sort(all(a))
#define Rev(a) reverse(all(a))
#define Uniq(a)                                                                \
  sort(all(a));                                                                \
  a.erase(unique(all(a)), end(a));
#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#define VEC(type, name, size)                                                  \
  vector<type> name(size);                                                     \
  in(name)
#define vv(type, name, h, ...)                                                 \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define VV(type, name, h, w)                                                   \
  vector<vector<type>> name(h, vector<type>(w));                               \
  in(name)
template <class T> inline const auto min(const T &a) {
  return *min_element(all(a));
}
template <class T> inline const auto max(const T &a) {
  return *max_element(all(a));
}
inline const ll popcnt(const ull a) { return __builtin_popcountll(a); }
inline const ll gcd(ll a, ll b) {
  while (b) {
    ll c = b;
    b = a % b;
    a = c;
  }
  return a;
}
inline const ll lcm(ll a, ll b) {
  unless(a && b) return 0;
  return a * b / gcd(a, b);
}
inline const ll intpow(ll a, ll b) {
  ll ans = 1;
  while (b) {
    if (b & 1)
      ans *= a;
    a *= a;
    b /= 2;
  }
  return ans;
}
inline const ll modpow(ll a, ll b, ll p = mod) {
  ll ans = 1;
  while (b) {
    if (b & 1)
      (ans *= a) %= p;
    (a *= a) %= p;
    b /= 2;
  }
  return ans;
}
template <class T, class U> inline const bool chmin(T &a, const U &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T, class U> inline const bool chmax(T &a, const U &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
inline const vector<ll> iota(const ll n) {
  vector<ll> a(n);
  iota(all(a), 0);
  return a;
}
inline const vector<pll> factor(ull x) {
  vector<pll> ans;
  for (ull i = 2; i * i <= x; i++)
    if (x % i == 0) {
      ans.push_back({i, 1});
      while ((x /= i) % i == 0)
        ans.back().second++;
    }
  if (x != 1)
    ans.push_back({x, 1});
  return ans;
}
inline const map<ll, ll> factor_map(ull x) {
  map<ll, ll> ans;
  for (ull i = 2; i * i <= x; i++)
    if (x % i == 0) {
      ans[i] = 1;
      while ((x /= i) % i == 0)
        ans[i]++;
    }
  if (x != 1)
    ans[x] = 1;
  return ans;
}
inline const vector<ll> divisor(ull x) {
  vector<ll> ans;
  for (ull i = 2; i * i <= x; i++)
    if (x % i == 0)
      ans.push_back(i);
  rrep(ans.size() - (ans.back() * ans.back() == x)) ans.push_back(x / ans[i]);
  return ans;
}
inline const int scan() { return getchar(); }
inline const void scan(int &a) { scanf("%d", &a); }
inline const void scan(unsigned &a) { scanf("%u", &a); }
inline const void scan(long &a) { scanf("%ld", &a); }
inline const void scan(long long &a) { scanf("%lld", &a); }
inline const void scan(char &a) {
  do {
    a = getchar();
  } while (a == ' ' || a == '\n');
}
inline const void scan(float &a) { scanf("%f", &a); }
inline const void scan(double &a) { scanf("%lf", &a); }
inline const void scan(long double &a) { scanf("%Lf", &a); }
inline const void scan(string &a) { cin >> a; }
template <class T> inline const void scan(vector<T> &a) {
  for (auto &&i : a)
    scan(i);
}
template <class T, size_t size> inline const void scan(array<T, size> &a) {
  for (auto &&i : a)
    scan(i);
}
template <class T, class L> inline const void scan(pair<T, L> &p) {
  scan(p.first);
  scan(p.second);
}
template <class T, size_t size> inline const void scan(T (&a)[size]) {
  for (auto &&i : a)
    scan(i);
}
inline const void in() {}
template <class Head, class... Tail>
inline const void in(Head &head, Tail &...tail) {
  scan(head);
  in(tail...);
}
inline const int ctoi(const char c) {
  if (c >= 'a' && c <= 'z') {
    return c - 'a';
  }
  if (c >= 'A' && c <= 'Z') {
    return c - 'A';
  }
  if (c >= '0' && c <= '9') {
    return c - '0';
  }
  return -1;
}
inline const void print() { putchar(' '); }
inline const void print(const bool a) { printf("%d", a); }
inline const void print(const int a) { printf("%d", a); }
inline const void print(const unsigned a) { printf("%u", a); }
inline const void print(const long a) { printf("%ld", a); }
inline const void print(const unsigned long long a) { printf("%llu", a); }
inline const void print(const char a) { printf("%c", a); }
inline const void print(const double a) { printf("%.15f", a); }
inline const void print(const long double a) { printf("%.15Lf", a); }
inline const void print(const string &a) {
  for (auto &&i : a)
    print(i);
}
template <class T> inline const void print(const vector<T> &a) {
  if (a.empty())
    return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    putchar(' ');
    print(*i);
  }
}
template <class T> inline const void print(const deque<T> &a) {
  if (a.empty())
    return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    putchar(' ');
    print(*i);
  }
}
template <class T, size_t size> inline const void print(const T (&a)[size]) {
  print(a[0]);
  for (auto i = a; ++i != end(a);) {
    putchar(' ');
    print(*i);
  }
}
template <class T> inline const void print(const T &a) { cout << a; }
inline const int out() {
  putchar('\n');
  return 0;
}
template <class T> inline const int out(const T &t) {
  print(t);
  putchar('\n');
  return 0;
}
template <class Head, class... Tail>
inline const int out(const Head &head, const Tail &...tail) {
  print(head);
  putchar(' ');
  out(tail...);
  return 0;
}
inline const int first(const bool i) { return out(i ? "first" : "second"); }
inline const int yes(const bool i) { return out(i ? "yes" : "no"); }
inline const int Yes(const bool i) { return out(i ? "Yes" : "No"); }
inline const int YES(const bool i) { return out(i ? "YES" : "NO"); }
inline const int possible(const bool i) {
  return out(i ? "possible" : "impossible");
}
inline const int Possible(const bool i) {
  return out(i ? "Possible" : "Impossible");
}
inline const int POSSIBLE(const bool i) {
  return out(i ? "POSSIBLE" : "IMPOSSIBLE");
}

using Graph = vector<vector<int>>;
using Graphw = vector<vector<pair<ll, ll>>>;
using mat = vector<vector<ll>>;
using vec = vector<ll>;

/*
namespace mp = boost::multiprecision;
// 任意長整数型
using Bint = mp::cpp_int;
// 仮数部長が32の浮動小数点数型
using Real32 = mp::number<mp::cpp_dec_float<32>>;
// 仮数部長が1024の浮動小数点数型
using Real1024 = mp::number<mp::cpp_dec_float<1024>>;
// 有理数型
using Rat = boost::rational<Bint>;
*/

namespace internal {

// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
  int x = 0;
  while ((1U << x) < (unsigned int)(n))
    x++;
  return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
  unsigned long index;
  _BitScanForward(&index, n);
  return index;
#else
  return __builtin_ctz(n);
#endif
}

} // namespace internal

template <class S, S (*op)(S, S), S (*e)()> struct segtree {
public:
  segtree() : segtree(0) {}
  segtree(int n) : segtree(std::vector<S>(n, e())) {}
  segtree(const std::vector<S> &v) : _n(int(v.size())) {
    log = internal::ceil_pow2(_n);
    size = 1 << log;
    d = std::vector<S>(2 * size, e());
    for (int i = 0; i < _n; i++)
      d[size + i] = v[i];
    for (int i = size - 1; i >= 1; i--) {
      update(i);
    }
  }

  void set(int p, S x) {
    assert(0 <= p && p < _n);
    p += size;
    d[p] = x;
    for (int i = 1; i <= log; i++)
      update(p >> i);
  }

  S get(int p) {
    assert(0 <= p && p < _n);
    return d[p + size];
  }

  S prod(int l, int r) {
    assert(0 <= l && l <= r && r <= _n);
    S sml = e(), smr = e();
    l += size;
    r += size;

    while (l < r) {
      if (l & 1)
        sml = op(sml, d[l++]);
      if (r & 1)
        smr = op(d[--r], smr);
      l >>= 1;
      r >>= 1;
    }
    return op(sml, smr);
  }

  S all_prod() { return d[1]; }

  template <bool (*f)(S)> int max_right(int l) {
    return max_right(l, [](S x) { return f(x); });
  }
  template <class F> int max_right(int l, F f) {
    assert(0 <= l && l <= _n);
    assert(f(e()));
    if (l == _n)
      return _n;
    l += size;
    S sm = e();
    do {
      while (l % 2 == 0)
        l >>= 1;
      if (!f(op(sm, d[l]))) {
        while (l < size) {
          l = (2 * l);
          if (f(op(sm, d[l]))) {
            sm = op(sm, d[l]);
            l++;
          }
        }
        return l - size;
      }
      sm = op(sm, d[l]);
      l++;
    } while ((l & -l) != l);
    return _n;
  }

  template <bool (*f)(S)> int min_left(int r) {
    return min_left(r, [](S x) { return f(x); });
  }
  template <class F> int min_left(int r, F f) {
    assert(0 <= r && r <= _n);
    assert(f(e()));
    if (r == 0)
      return 0;
    r += size;
    S sm = e();
    do {
      r--;
      while (r > 1 && (r % 2))
        r >>= 1;
      if (!f(op(d[r], sm))) {
        while (r < size) {
          r = (2 * r + 1);
          if (f(op(d[r], sm))) {
            sm = op(d[r], sm);
            r--;
          }
        }
        return r + 1 - size;
      }
      sm = op(d[r], sm);
    } while ((r & -r) != r);
    return 0;
  }

private:
  int _n, size, log;
  std::vector<S> d;

  void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};

int op(int a, int b) { return max(a, b); }
int e() { return 0; }
int v;

bool f(int a) { return a < v; }

signed main() {

  INT(N, Q);
  segtree<int, op, e> seg(N);
  rep(i, N) {
    INT(A);
    seg.set(i, A);
  }
  vector<int> ans;
  rep(i, Q) {
    INT(T);
    if (T == 1) {
      INT(X, V);
      X--;
      seg.set(X, V);
    }
    elif (T == 2) {
      INT(L, R);
      L--;
      R--;
      ans.push_back(seg.prod(L, R + 1));
    }
    else {
      INT(X, V);
      v = V;
      X--;
      ans.push_back(seg.max_right<f>(X) + 1);
    }
  }
  rep(i, ans.size()) out(ans[i]);
}


Fixed submission:
/*
#include <boost/multiprecision/cpp_dec_float.hpp>
#include <boost/multiprecision/cpp_int.hpp>

#include <boost/rational.hpp>
*/
// #include <atcoder/all>
#include <bits/stdc++.h>
using namespace std;
// using namespace atcoder;
#define _GLIBCXX_DEBUG
#define rep(i, t) for (ll i = (ll)(0); i < (ll)(t); i++)
#define rep2(i, s, t) for (ll i = (ll)(s); i < (ll)(t); i++)
#define rep3(i, t) for (ll i = (ll)(1); i <= (ll)(t); i++)
#define rep4(i, s, t) for (ll i = (ll)(s); i <= (ll)(t); i++)
#define repr(i, t) for (ll i = (t - 1); i >= (0); i--)
#define repr2(i, s, t) for (ll i = (t - 1); i >= (s); i--)
#define repr3(i, t) for (ll i = (t); i >= (1); i--)
#define repr4(i, s, t) for (ll i = (t); i >= (s); i--)
using ll = long long;
using ld = long double;
using ull = unsigned long long;
using uint = unsigned;
using pcc = pair<char, char>;
using pll = pair<ll, ll>;
using pii = pair<int, int>;
using pdd = pair<double, double>;
using tuplis = array<ll, 3>;
template <class T> using pq = priority_queue<T, vector<T>, greater<T>>;
inline const ll LINF = 1e18;
inline const ll MINF = 1e15;
inline const int INF = 1e9 + 1e5;
inline const int mod = 1000000007;
// inline const int mod=998244353;

inline const ld DINF = numeric_limits<ld>::infinity();
inline const ld EPS = 1e-9;
inline const ld PI = acos(-1);
// const ll dx[] ={0,1,0,-1,1,-1,1,-1};
// const ll dy[] ={1,0,-1,0,1,1,-1,-1};
inline const bool ingrid(const int i, const int j, const int H, const int W) {
  return i >= 0 && i < H && j >= 0 && j < W;
}
inline const ll dx[] = {0, 1, 0, -1};
inline const ll dy[] = {1, 0, -1, 0};
inline const bool is_low(char c) { return ('a' <= c) && (c <= 'z'); }
inline const bool is_upp(char c) { return ('A' <= c) && (c <= 'Z'); }
#define each1(i, a) for (auto &&i : a)
#define each2(x, y, a) for (auto &&[x, y] : a)
#define each3(x, y, z, a) for (auto &&[x, y, z] : a)
#define rrep(n) for (ll i = (n); i--;)
#define stlen(s) ll s.size() - 1
#define all(v) begin(v), end(v)
#define range(v, a) begin(v), begin(v) + a
#define range2(v, a, b) begin(v) + a, begin(v) + b
#define range3(v, a) begin(v) + 1, begin(v) + a + 1
#define range4(v, a, b) begin(v) + a + 1, begin(v) + b + 1
#define allr(v) rbegin(v), v.rend(v)
#define ranger(v, a) rbegin(v), rbegin(v) + a
#define ranger2(v, a, b) rbegin(v) + a, rbegin(v) + b
#define ranger3(v, a) rbegin(v) + 1, rbegin(v) + a + 1
#define ranger4(v, a, b) rbegin(v) + a + 1, rbegin(v) + b + 1
#define cout(n) cout << std::fixed << std::setprecision(n)
// #define sum(...) accumulate(all(__VA_ARGS__),0LL)
#define dsum(...) accumulate(all(__VA_ARGS__), 0.0L)
#define elif else if
#define unless(a) if (!(a))
#define mp make_pair
#define mt make_tuple
#define INT(...)                                                               \
  int __VA_ARGS__;                                                             \
  in(__VA_ARGS__)
#define LL(...)                                                                \
  ll __VA_ARGS__;                                                              \
  in(__VA_ARGS__)
#define ULL(...)                                                               \
  ull __VA_ARGS__;                                                             \
  in(__VA_ARGS__)
#define STR(...)                                                               \
  string __VA_ARGS__;                                                          \
  in(__VA_ARGS__)
#define CHR(...)                                                               \
  char __VA_ARGS__;                                                            \
  in(__VA_ARGS__)
#define DBL(...)                                                               \
  double __VA_ARGS__;                                                          \
  in(__VA_ARGS__)
#define LD(...)                                                                \
  ld __VA_ARGS__;                                                              \
  in(__VA_ARGS__)
#define Sort(a) sort(all(a))
#define Rev(a) reverse(all(a))
#define Uniq(a)                                                                \
  sort(all(a));                                                                \
  a.erase(unique(all(a)), end(a));
#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#define VEC(type, name, size)                                                  \
  vector<type> name(size);                                                     \
  in(name)
#define vv(type, name, h, ...)                                                 \
  vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define VV(type, name, h, w)                                                   \
  vector<vector<type>> name(h, vector<type>(w));                               \
  in(name)
template <class T> inline const auto min(const T &a) {
  return *min_element(all(a));
}
template <class T> inline const auto max(const T &a) {
  return *max_element(all(a));
}
inline const ll popcnt(const ull a) { return __builtin_popcountll(a); }
inline const ll gcd(ll a, ll b) {
  while (b) {
    ll c = b;
    b = a % b;
    a = c;
  }
  return a;
}
inline const ll lcm(ll a, ll b) {
  unless(a && b) return 0;
  return a * b / gcd(a, b);
}
inline const ll intpow(ll a, ll b) {
  ll ans = 1;
  while (b) {
    if (b & 1)
      ans *= a;
    a *= a;
    b /= 2;
  }
  return ans;
}
inline const ll modpow(ll a, ll b, ll p = mod) {
  ll ans = 1;
  while (b) {
    if (b & 1)
      (ans *= a) %= p;
    (a *= a) %= p;
    b /= 2;
  }
  return ans;
}
template <class T, class U> inline const bool chmin(T &a, const U &b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}
template <class T, class U> inline const bool chmax(T &a, const U &b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}
inline const vector<ll> iota(const ll n) {
  vector<ll> a(n);
  iota(all(a), 0);
  return a;
}
inline const vector<pll> factor(ull x) {
  vector<pll> ans;
  for (ull i = 2; i * i <= x; i++)
    if (x % i == 0) {
      ans.push_back({i, 1});
      while ((x /= i) % i == 0)
        ans.back().second++;
    }
  if (x != 1)
    ans.push_back({x, 1});
  return ans;
}
inline const map<ll, ll> factor_map(ull x) {
  map<ll, ll> ans;
  for (ull i = 2; i * i <= x; i++)
    if (x % i == 0) {
      ans[i] = 1;
      while ((x /= i) % i == 0)
        ans[i]++;
    }
  if (x != 1)
    ans[x] = 1;
  return ans;
}
inline const vector<ll> divisor(ull x) {
  vector<ll> ans;
  for (ull i = 2; i * i <= x; i++)
    if (x % i == 0)
      ans.push_back(i);
  rrep(ans.size() - (ans.back() * ans.back() == x)) ans.push_back(x / ans[i]);
  return ans;
}
inline const int scan() { return getchar(); }
inline const void scan(int &a) { scanf("%d", &a); }
inline const void scan(unsigned &a) { scanf("%u", &a); }
inline const void scan(long &a) { scanf("%ld", &a); }
inline const void scan(long long &a) { scanf("%lld", &a); }
inline const void scan(char &a) {
  do {
    a = getchar();
  } while (a == ' ' || a == '\n');
}
inline const void scan(float &a) { scanf("%f", &a); }
inline const void scan(double &a) { scanf("%lf", &a); }
inline const void scan(long double &a) { scanf("%Lf", &a); }
inline const void scan(string &a) { cin >> a; }
template <class T> inline const void scan(vector<T> &a) {
  for (auto &&i : a)
    scan(i);
}
template <class T, size_t size> inline const void scan(array<T, size> &a) {
  for (auto &&i : a)
    scan(i);
}
template <class T, class L> inline const void scan(pair<T, L> &p) {
  scan(p.first);
  scan(p.second);
}
template <class T, size_t size> inline const void scan(T (&a)[size]) {
  for (auto &&i : a)
    scan(i);
}
inline const void in() {}
template <class Head, class... Tail>
inline const void in(Head &head, Tail &...tail) {
  scan(head);
  in(tail...);
}
inline const int ctoi(const char c) {
  if (c >= 'a' && c <= 'z') {
    return c - 'a';
  }
  if (c >= 'A' && c <= 'Z') {
    return c - 'A';
  }
  if (c >= '0' && c <= '9') {
    return c - '0';
  }
  return -1;
}
inline const void print() { putchar(' '); }
inline const void print(const bool a) { printf("%d", a); }
inline const void print(const int a) { printf("%d", a); }
inline const void print(const unsigned a) { printf("%u", a); }
inline const void print(const long a) { printf("%ld", a); }
inline const void print(const unsigned long long a) { printf("%llu", a); }
inline const void print(const char a) { printf("%c", a); }
inline const void print(const double a) { printf("%.15f", a); }
inline const void print(const long double a) { printf("%.15Lf", a); }
inline const void print(const string &a) {
  for (auto &&i : a)
    print(i);
}
template <class T> inline const void print(const vector<T> &a) {
  if (a.empty())
    return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    putchar(' ');
    print(*i);
  }
}
template <class T> inline const void print(const deque<T> &a) {
  if (a.empty())
    return;
  print(a[0]);
  for (auto i = a.begin(); ++i != a.end();) {
    putchar(' ');
    print(*i);
  }
}
template <class T, size_t size> inline const void print(const T (&a)[size]) {
  print(a[0]);
  for (auto i = a; ++i != end(a);) {
    putchar(' ');
    print(*i);
  }
}
template <class T> inline const void print(const T &a) { cout << a; }
inline const int out() {
  putchar('\n');
  return 0;
}
template <class T> inline const int out(const T &t) {
  print(t);
  putchar('\n');
  return 0;
}
template <class Head, class... Tail>
inline const int out(const Head &head, const Tail &...tail) {
  print(head);
  putchar(' ');
  out(tail...);
  return 0;
}
inline const int first(const bool i) { return out(i ? "first" : "second"); }
inline const int yes(const bool i) { return out(i ? "yes" : "no"); }
inline const int Yes(const bool i) { return out(i ? "Yes" : "No"); }
inline const int YES(const bool i) { return out(i ? "YES" : "NO"); }
inline const int possible(const bool i) {
  return out(i ? "possible" : "impossible");
}
inline const int Possible(const bool i) {
  return out(i ? "Possible" : "Impossible");
}
inline const int POSSIBLE(const bool i) {
  return out(i ? "POSSIBLE" : "IMPOSSIBLE");
}

using Graph = vector<vector<int>>;
using Graphw = vector<vector<pair<ll, ll>>>;
using mat = vector<vector<ll>>;
using vec = vector<ll>;

/*
namespace mp = boost::multiprecision;
// 任意長整数型
using Bint = mp::cpp_int;
// 仮数部長が32の浮動小数点数型
using Real32 = mp::number<mp::cpp_dec_float<32>>;
// 仮数部長が1024の浮動小数点数型
using Real1024 = mp::number<mp::cpp_dec_float<1024>>;
// 有理数型
using Rat = boost::rational<Bint>;
*/

namespace internal {

// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
  int x = 0;
  while ((1U << x) < (unsigned int)(n))
    x++;
  return x;
}

// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
#ifdef _MSC_VER
  unsigned long index;
  _BitScanForward(&index, n);
  return index;
#else
  return __builtin_ctz(n);
#endif
}

} // namespace internal

template <class S, S (*op)(S, S), S (*e)()> struct segtree {
public:
  segtree() : segtree(0) {}
  segtree(int n) : segtree(std::vector<S>(n, e())) {}
  segtree(const std::vector<S> &v) : _n(int(v.size())) {
    log = internal::ceil_pow2(_n);
    size = 1 << log;
    d = std::vector<S>(2 * size, e());
    for (int i = 0; i < _n; i++)
      d[size + i] = v[i];
    for (int i = size - 1; i >= 1; i--) {
      update(i);
    }
  }

  void set(int p, S x) {
    assert(0 <= p && p < _n);
    p += size;
    d[p] = x;
    for (int i = 1; i <= log; i++)
      update(p >> i);
  }

  S get(int p) {
    assert(0 <= p && p < _n);
    return d[p + size];
  }

  S prod(int l, int r) {
    assert(0 <= l && l <= r && r <= _n);
    S sml = e(), smr = e();
    l += size;
    r += size;

    while (l < r) {
      if (l & 1)
        sml = op(sml, d[l++]);
      if (r & 1)
        smr = op(d[--r], smr);
      l >>= 1;
      r >>= 1;
    }
    return op(sml, smr);
  }

  S all_prod() { return d[1]; }

  template <bool (*f)(S)> int max_right(int l) {
    return max_right(l, [](S x) { return f(x); });
  }
  template <class F> int max_right(int l, F f) {
    assert(0 <= l && l <= _n);
    assert(f(e()));
    if (l == _n)
      return _n;
    l += size;
    S sm = e();
    do {
      while (l % 2 == 0)
        l >>= 1;
      if (!f(op(sm, d[l]))) {
        while (l < size) {
          l = (2 * l);
          if (f(op(sm, d[l]))) {
            sm = op(sm, d[l]);
            l++;
          }
        }
        return l - size;
      }
      sm = op(sm, d[l]);
      l++;
    } while ((l & -l) != l);
    return _n;
  }

  template <bool (*f)(S)> int min_left(int r) {
    return min_left(r, [](S x) { return f(x); });
  }
  template <class F> int min_left(int r, F f) {
    assert(0 <= r && r <= _n);
    assert(f(e()));
    if (r == 0)
      return 0;
    r += size;
    S sm = e();
    do {
      r--;
      while (r > 1 && (r % 2))
        r >>= 1;
      if (!f(op(d[r], sm))) {
        while (r < size) {
          r = (2 * r + 1);
          if (f(op(d[r], sm))) {
            sm = op(d[r], sm);
            r--;
          }
        }
        return r + 1 - size;
      }
      sm = op(d[r], sm);
    } while ((r & -r) != r);
    return 0;
  }

private:
  int _n, size, log;
  std::vector<S> d;

  void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }
};

int op(int a, int b) { return max(a, b); }
int e() { return -1; }
int v;

bool f(int a) { return a < v; }

signed main() {

  INT(N, Q);
  segtree<int, op, e> seg(N);
  rep(i, N) {
    INT(A);
    seg.set(i, A);
  }
  vector<int> ans;
  rep(i, Q) {
    INT(T);
    if (T == 1) {
      INT(X, V);
      X--;
      seg.set(X, V);
    }
    elif (T == 2) {
      INT(L, R);
      L--;
      R--;
      ans.push_back(seg.prod(L, R + 1));
    }
    else {
      INT(X, V);
      v = V;
      X--;
      ans.push_back(seg.max_right<f>(X) + 1);
    }
  }
  rep(i, ans.size()) out(ans[i]);
}