#ifdef LOCAL #include "template.hpp" #else #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; namespace io { template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } template istream &operator>>(istream &is, array &v) { for (auto &x : v) is >> x; return is; } template istream& cin_tuple_impl(istream &is, T &t) { if constexpr (N < std::tuple_size::value) { auto &x = std::get(t); is >> x; cin_tuple_impl(is, t); } return is; } template istream &operator>>(istream &is, tuple &t) { return cin_tuple_impl(is, t); } template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template ostream &operator<<(ostream &os, const array &v) { size_t n = v.size(); for (size_t i = 0; i < n; i++) { if (i) os << " "; os << v[i]; } return os; } template ostream& cout_tuple_impl(ostream &os, const T &t) { if constexpr (N < std::tuple_size::value) { if constexpr (N > 0) os << " "; const auto &x = std::get(t); os << x; cout_tuple_impl(os, t); } return os; } template ostream &operator<<(ostream &os, const tuple &t) { return cout_tuple_impl(os, t); } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } void outr() {} template void outr(const T &t, const U &...u) { cout << t; outr(u...); } void __attribute__((constructor)) _c() { ios_base::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15); } } // namespace io using io::in; using io::out; using io::outr; #define SHOW(x) static_cast(0) using ll = long long; using D = double; using LD = long double; using P = pair; using u8 = uint8_t; using u16 = uint16_t; using u32 = uint32_t; using u64 = uint64_t; using i128 = __int128; using u128 = unsigned __int128; using vi = vector; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; template using vvvvvc = vector>; #define vv(type, name, h, ...) \ vector> name(h, vector(__VA_ARGS__)) #define vvv(type, name, h, w, ...) \ vector>> name( \ h, vector>(w, vector(__VA_ARGS__))) #define vvvv(type, name, a, b, c, ...) \ vector>>> name( \ a, vector>>( \ b, vector>(c, vector(__VA_ARGS__)))) template using PQ = priority_queue>; template using minPQ = priority_queue, greater>; #define rep1(a) for(ll i = 0; i < a; i++) #define rep2(i, a) for(ll i = 0; i < a; i++) #define rep3(i, a, b) for(ll i = a; i < b; i++) #define rep4(i, a, b, c) for(ll i = a; i < b; i += c) #define overload4(a, b, c, d, e, ...) e #define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__) #define rrep1(a) for(ll i = (a)-1; i >= 0; i--) #define rrep2(i, a) for(ll i = (a)-1; i >= 0; i--) #define rrep3(i, a, b) for(ll i = (b)-1; i >= a; i--) #define rrep4(i, a, b, c) for(ll i = (b)-1; i >= a; i -= c) #define rrep(...) overload4(__VA_ARGS__, rrep4, rrep3, rrep2, rrep1)(__VA_ARGS__) #define for_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s))) #define ALL(v) v.begin(), v.end() #define RALL(v) v.rbegin(), v.rend() #define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() ) #define SZ(v) ll(v.size()) #define MIN(v) *min_element(ALL(v)) #define MAX(v) *max_element(ALL(v)) #define LB(c, x) distance((c).begin(), lower_bound(ALL(c), (x))) #define UB(c, x) distance((c).begin(), upper_bound(ALL(c), (x))) template T SUM(const vector &v) { T res = 0; for(auto &&a : v) res += a; return res; } template vector> RLE(const vector &v) { if (v.empty()) return {}; T cur = v.front(); int cnt = 1; vector> res; for (int i = 1; i < (int)v.size(); i++) { if (cur == v[i]) cnt++; else { res.emplace_back(cur, cnt); cnt = 1; cur = v[i]; } } res.emplace_back(cur, cnt); return res; } template inline bool chmax(T &a, const S &b) { return (a < b ? a = b, true : false); } template inline bool chmin(T &a, const S &b) { return (a > b ? a = b, true : false); } void YESNO(bool flag) { out(flag ? "YES" : "NO"); } void yesno(bool flag) { out(flag ? "Yes" : "No"); } int popcnt(int x) { return __builtin_popcount(x); } int popcnt(u32 x) { return __builtin_popcount(x); } int popcnt(ll x) { return __builtin_popcountll(x); } int popcnt(u64 x) { return __builtin_popcountll(x); } int popcnt_sgn(int x) { return (__builtin_parity(x) & 1 ? -1 : 1); } int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); } int popcnt_sgn(ll x) { return (__builtin_parityl(x) & 1 ? -1 : 1); } int popcnt_sgn(u64 x) { return (__builtin_parityl(x) & 1 ? -1 : 1); } int highbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int highbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); } int highbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int highbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); } int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); } int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); } template T get_bit(T x, int k) { return x >> k & 1; } template T set_bit(T x, int k) { return x | T(1) << k; } template T reset_bit(T x, int k) { return x & ~(T(1) << k); } template T flip_bit(T x, int k) { return x ^ T(1) << k; } template T popf(deque &que) { T a = que.front(); que.pop_front(); return a; } template T popb(deque &que) { T a = que.back(); que.pop_back(); return a; } template T pop(queue &que) { T a = que.front(); que.pop(); return a; } template T pop(stack &que) { T a = que.top(); que.pop(); return a; } template T pop(PQ &que) { T a = que.top(); que.pop(); return a; } template T pop(minPQ &que) { T a = que.top(); que.pop(); return a; } template ll binary_search(F check, ll ok, ll ng, bool check_ok = true) { if (check_ok) assert(check(ok)); while (abs(ok - ng) > 1) { ll mid = (ok + ng) / 2; (check(mid) ? ok : ng) = mid; } return ok; } template double binary_search_real(F check, double ok, double ng, int iter = 60) { for (int _ = 0; _ < iter; _++) { double mid = (ok + ng) / 2; (check(mid) ? ok : ng) = mid; } return (ok + ng) / 2; } // max x s.t. b*x <= a ll div_floor(ll a, ll b) { assert(b != 0); if (b < 0) a = -a, b = -b; return a / b - (a % b < 0); } // max x s.t. b*x < a ll div_under(ll a, ll b) { assert(b != 0); if (b < 0) a = -a, b = -b; return a / b - (a % b <= 0); } // min x s.t. b*x >= a ll div_ceil(ll a, ll b) { assert(b != 0); if (b < 0) a = -a, b = -b; return a / b + (a % b > 0); } // min x s.t. b*x > a ll div_over(ll a, ll b) { assert(b != 0); if (b < 0) a = -a, b = -b; return a / b + (a % b >= 0); } // x = a mod b (b > 0), 0 <= x < b ll modulo(ll a, ll b) { assert(b > 0); ll c = a % b; return c < 0 ? c + b : c; } // (q,r) s.t. a = b*q + r, 0 <= r < b (b > 0) // div_floor(a,b), modulo(a,b) pair divmod(ll a, ll b) { ll q = div_floor(a,b); return {q, a - b*q}; } #endif struct WordSizeTree{ using u32 = uint32_t; using u64 = uint64_t; inline int lowbit(u64 x) { return x ? __builtin_ctzll(x) : -1; } inline int highbit(u64 x) { return x ? 63 - __builtin_clzll(x) : -1; } static constexpr u32 B = 64; int n, log; vector> seg; WordSizeTree() {} WordSizeTree(int n_) { build(n_); } template WordSizeTree(int n_, F f) { build(n_, f); } void build(int sz) { seg.clear(); n = sz; do { seg.emplace_back(vector((sz+B-1)/B)); sz = (sz+B-1)/B; } while(sz > 1); log = seg.size(); } template void build(int sz, F f) { build(sz); for (int i = 0; i < n; i++) seg[0][i/B] |= u64(f(i) << (i%B)); for (int h = 0; h < log-1; h++) { for (int i = 0; i < (int)seg[h].size(); i++) { seg[h+1][i/B] |= u64(bool(seg[h][i])) << (i%B); } } } int size() const { return n; } bool operator[] (int i) const { return seg[0][i/B] >> (i%B) & 1; } void insert(int i) { assert(0 <= i and i < n); for (int h = 0; h < log; h++) { seg[h][i/B] |= u64(1) << (i%B), i /= B; } } void erase(int i) { assert(0 <= i and i < n); u64 x = 0; for (int h = 0; h < log; h++) { seg[h][i/B] &= ~(u64(1) << (i%B)); seg[h][i/B] |= x << (i%B); x = bool(seg[h][i/B]); i /= B; } } // min x s.t. (x >= i) and (x in S), or n if no such x exists int next(int i) { assert(i <= n); if (i < 0) i = 0; for (int h = 0; h < log; h++) { if (i/B == seg[h].size()) break; u64 d = seg[h][i/B] >> (i%B); if (!d) { i = i/B+1; continue; } i += lowbit(d); for (int g = h-1; g >= 0; g--) { i *= B; i += lowbit(seg[g][i/B]); } return i; } return n; } // max x s.t. (x <= i) and (x in S), or -1 if no such x exists int prev(int i) { assert(i >= -1); if (i >= n) i = n-1; for (int h = 0; h < log; h++) { if (i == -1) break; u64 d = seg[h][i/B] << (63-i%B); if (!d) { i = i/B-1; continue; } i -= __builtin_clzll(d); for (int g = h-1; g >= 0; g--) { i *= B; i += highbit(seg[g][i/B]); } return i; } return -1; } }; struct Mo{ int n,q,w; vector l,r,ord; Mo(int N, int Q): n(N), q(Q), ord(Q) { w = max(1, 1.0 * N / max(1.0, sqrt(Q * 2.0 / 3.0))); iota(ALL(ord),0); } void insert(int x, int y){ // [x, y) l.emplace_back(x); r.emplace_back(y); } template void build(const AL &add_left, const AR &add_right, const DL &del_left, const DR &del_right, const CA &calc_ans){ sort(ALL(ord), [&](int i, int j){ if((l[i]/w != l[j]/w)) return l[i] < l[j]; if(l[i]/w & 1) return r[i] > r[j]; return r[i] < r[j]; }); int nl = 0, nr = 0; for(int i : ord){ while(nr > r[i]) del_right(--nr); while(nl < l[i]) del_left(nl++); while(nl > l[i]) add_left(--nl); while(nr < r[i]) add_right(nr++); calc_ans(i); } } }; constexpr int mx = 1 << 20; void solve() { int n,q; in(n,q); vc a(n); in(a); vc fa(mx); WordSizeTree sa(mx); vc fadj(mx); WordSizeTree sadj(mx); int num_double = 0; auto adj_add = [&](int x) { if(fadj[x]++ == 0) sadj.insert(x); }; auto adj_del = [&](int x) { if(--fadj[x] == 0) sadj.erase(x); }; auto a_add = [&](int x) { if(fa[x] == 0) { int sp = sa.prev(x); int sn = sa.next(x); if (sp != -1 and sn != mx) adj_del(sp ^ sn); if (sp != -1) adj_add(x ^ sp); if (sn != mx) adj_add(x ^ sn); sa.insert(x); } else if(fa[x] == 1) { num_double++; } fa[x]++; }; auto a_del = [&](int x) { if(fa[x] == 1) { int sp = sa.prev(x); int sn = sa.next(x); if (sp != -1) adj_del(x ^ sp); if (sn != mx) adj_del(x ^ sn); if (sp != -1 and sn != mx) adj_add(sp ^ sn); sa.erase(x); } else if(fa[x] == 2) { num_double--; } fa[x]--; }; vc> query(q, {-1,-1,-1}); vc ans; int cur = 0; auto add_left = [&](int idx){ auto [pos, del, add] = query[idx]; if(pos == -1) return; // out("addL", idx); assert(a[pos] == add); if(pos < cur) { a_del(add); a_add(del); } a[pos] = del; }; auto add_right = [&](int idx){ // out("addR", idx, a[idx]); a_add(a[idx]); cur++; }; auto del_left = [&](int idx){ auto [pos, del, add] = query[idx]; if(pos == -1) return; // out("delL", idx); assert(a[pos] == del); if(pos < cur) { a_del(del); a_add(add); } a[pos] = add; }; auto del_right = [&](int idx){ // out("delR", idx, a[idx]); a_del(a[idx]); cur--; }; auto calc_ans = [&](int idx){ // out("ans", idx); if(num_double > 0) ans[idx] = 0; else ans[idx] = sadj.next(0); }; vc tmp = a; int qq = 0; vc

mo_ins; rep(i,q){ int op; in(op); if(op == 1){ int idx, x; in(idx, x); idx--; query[i] = {idx, tmp[idx], x}; tmp[idx] = x; } else{ int r; in(r); mo_ins.emplace_back(i,r); qq++; } } Mo mo(n,qq); for(auto [l,r] : mo_ins) mo.insert(l, r); ans.resize(qq); mo.build(add_left, add_right, del_left, del_right, calc_ans); rep(i,qq) out(ans[i]); } int main() { int tc = 1; // in(tc); while(tc--){ solve(); } }