結果
| 問題 | No.3792 XOR^2 Sum Query |
| コンテスト | |
| ユーザー |
👑  Forested
|
| 提出日時 | 2026-11-06 22:47:18 |
| 言語 | C++23 (gcc 15.3.0 + boost 1.92.0 + ACL) |
| 結果 |
AC
不安定
|
| 実行時間 | 2,434 ms / 3,000 ms |
| + 835µs | |
| コード長 | 18,154 bytes |
| 記録 | |
| コンパイル時間 | 2,662 ms |
| コンパイル使用メモリ | 343,780 KB |
| 実行使用メモリ | 136,436 KB |
| 最終ジャッジ日時 | 2026-11-06 22:48:38 |
| 合計ジャッジ時間 | 71,903 ms |
|
ジャッジサーバーID （参考情報） |
judge7_0 / judge4_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 35 |
ソースコード
#ifndef LOCAL
#define FAST_IO
#endif
// ============
#include <bits/stdc++.h>
#define OVERRIDE(a, b, c, d, ...) d
#define REP2(i, n) for (i32 i = 0; i < (i32)(n); ++i)
#define REP3(i, m, n) for (i32 i = (i32)(m); i < (i32)(n); ++i)
#define REP(...) OVERRIDE(__VA_ARGS__, REP3, REP2)(__VA_ARGS__)
#define PER2(i, n) for (i32 i = (i32)(n)-1; i >= 0; --i)
#define PER3(i, m, n) for (i32 i = (i32)(n)-1; i >= (i32)(m); --i)
#define PER(...) OVERRIDE(__VA_ARGS__, PER3, PER2)(__VA_ARGS__)
#define ALL(x) begin(x), end(x)
#define LEN(x) (i32)(x.size())
using namespace std;
using u32 = unsigned int;
using u64 = unsigned long long;
using i32 = signed int;
using i64 = signed long long;
using f64 = double;
using f80 = long double;
using pi = pair<i32, i32>;
using pl = pair<i64, i64>;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = V<V<T>>;
template <typename T>
using VVV = V<V<V<T>>>;
template <typename T>
using VVVV = V<V<V<V<T>>>>;
template <typename T>
using PQR = priority_queue<T, V<T>, greater<T>>;
template <typename T>
bool chmin(T &x, const T &y) {
if (x > y) {
x = y;
return true;
}
return false;
}
template <typename T>
bool chmax(T &x, const T &y) {
if (x < y) {
x = y;
return true;
}
return false;
}
template <typename T>
i32 lob(const V<T> &arr, const T &v) {
return (i32)(lower_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
i32 upb(const V<T> &arr, const T &v) {
return (i32)(upper_bound(ALL(arr), v) - arr.begin());
}
template <typename T>
V<i32> argsort(const V<T> &arr) {
V<i32> ret(arr.size());
iota(ALL(ret), 0);
sort(ALL(ret), [&](i32 i, i32 j) -> bool {
if (arr[i] == arr[j]) {
return i < j;
} else {
return arr[i] < arr[j];
}
});
return ret;
}
#ifdef INT128
using u128 = __uint128_t;
using i128 = __int128_t;
#endif
[[maybe_unused]] constexpr i32 INF = 1000000100;
[[maybe_unused]] constexpr i64 INF64 = 3000000000000000100;
struct SetUpIO {
SetUpIO() {
#ifdef FAST_IO
ios::sync_with_stdio(false);
cin.tie(nullptr);
#endif
cout << fixed << setprecision(15);
}
} set_up_io;
void scan(char &x) { cin >> x; }
void scan(u32 &x) { cin >> x; }
void scan(u64 &x) { cin >> x; }
void scan(i32 &x) { cin >> x; }
void scan(i64 &x) { cin >> x; }
void scan(f64 &x) { cin >> x; }
void scan(string &x) { cin >> x; }
template <typename T>
void scan(V<T> &x) {
for (T &ele : x) {
scan(ele);
}
}
void read() {}
template <typename Head, typename... Tail>
void read(Head &head, Tail &...tail) {
scan(head);
read(tail...);
}
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__);
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__);
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__);
#define I32(...) \
i32 __VA_ARGS__; \
read(__VA_ARGS__);
#define I64(...) \
i64 __VA_ARGS__; \
read(__VA_ARGS__);
#define F64(...) \
f64 __VA_ARGS__; \
read(__VA_ARGS__);
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__);
#define VEC(type, name, size) \
V<type> name(size); \
read(name);
#define VVEC(type, name, size1, size2) \
VV<type> name(size1, V<type>(size2)); \
read(name);
// ============
#ifdef DEBUGF
#else
#define DBG(...) (void)0
#endif
// ============
#include <cassert>
#include <utility>
#include <vector>
// ============
#include <algorithm>
#include <limits>
#include <utility>
template <typename T>
struct Add {
using Value = T;
static Value id() { return T(0); }
static Value op(const Value &lhs, const Value &rhs) { return lhs + rhs; }
static Value inv(const Value &x) { return -x; }
};
template <typename T>
struct Mul {
using Value = T;
static Value id() { return Value(1); }
static Value op(const Value &lhs, const Value &rhs) { return lhs * rhs; }
static Value inv(const Value &x) { return Value(1) / x; }
};
template <typename T>
struct Min {
static_assert(std::numeric_limits<T>::is_specialized);
using Value = T;
static Value id() { return std::numeric_limits<T>::max(); }
static Value op(const Value &lhs, const Value &rhs) {
return std::min(lhs, rhs);
}
};
template <typename T>
struct Max {
static_assert(std::numeric_limits<T>::is_specialized);
using Value = T;
static Value id() { return std::numeric_limits<Value>::min(); }
static Value op(const Value &lhs, const Value &rhs) {
return std::max(lhs, rhs);
}
};
template <typename T>
struct Xor {
using Value = T;
static Value id() { return T(0); }
static Value op(const Value &lhs, const Value &rhs) { return lhs ^ rhs; }
static Value inv(const Value &x) { return x; }
};
template <typename Monoid>
struct Reversible {
using Value = std::pair<typename Monoid::Value, typename Monoid::Value>;
static Value id() { return Value(Monoid::id(), Monoid::id()); }
static Value op(const Value &v1, const Value &v2) {
return Value(Monoid::op(v1.first, v2.first),
Monoid::op(v2.second, v1.second));
}
};
// ============
template <typename Monoid>
class SegmentTree {
public:
using Value = typename Monoid::Value;
private:
int old_length;
int length;
std::vector<Value> node;
static int ceil2(int n) {
int l = 1;
while (l < n) {
l <<= 1;
}
return l;
}
public:
SegmentTree(int n)
: old_length(n),
length(ceil2(old_length)),
node(length << 1, Monoid::id()) {
assert(n >= 0);
}
SegmentTree(const std::vector<Value> &v)
: old_length((int)v.size()),
length(ceil2(old_length)),
node(length << 1, Monoid::id()) {
for (int i = 0; i < old_length; ++i) {
node[i + length] = v[i];
}
for (int i = length - 1; i > 0; --i) {
node[i] = Monoid::op(node[i << 1], node[i << 1 | 1]);
}
}
template <typename F>
SegmentTree(int n, const F &f)
: old_length(n), length(ceil2(n)), node(length << 1, Monoid::id()) {
assert(n >= 0);
for (int i = 0; i < old_length; ++i) {
node[i + length] = f(i);
}
for (int i = length - 1; i > 0; --i) {
node[i] = Monoid::op(node[i << 1], node[i << 1 | 1]);
}
}
const Value &operator[](int idx) const {
assert(idx >= 0 && idx < old_length);
return node[idx + length];
}
void update(int idx, Value val) {
assert(idx >= 0 && idx < old_length);
idx += length;
node[idx] = std::move(val);
while (idx != 1) {
idx >>= 1;
node[idx] = Monoid::op(node[idx << 1], node[idx << 1 | 1]);
}
}
Value prod(int l, int r) const {
assert(l >= 0 && l <= r && r <= old_length);
Value prodl = Monoid::id();
Value prodr = Monoid::id();
l += length;
r += length;
while (l != r) {
if (l & 1) {
prodl = Monoid::op(prodl, node[l++]);
}
if (r & 1) {
prodr = Monoid::op(node[--r], prodr);
}
l >>= 1;
r >>= 1;
}
return Monoid::op(prodl, prodr);
}
Value all_prod() const { return node[1]; }
template <typename F>
int max_right(int l, F f) const {
assert(0 <= l && l <= old_length);
assert(f(Monoid::id()));
if (l == old_length) {
return old_length;
}
l += length;
Value prod = Monoid::id();
do {
while (!(l & 1)) {
l >>= 1;
}
if (!f(Monoid::op(prod, node[l]))) {
while (l < length) {
l <<= 1;
if (f(Monoid::op(prod, node[l]))) {
prod = Monoid::op(prod, node[l++]);
}
}
return l - length;
}
prod = Monoid::op(prod, node[l++]);
} while ((l & -l) != l);
return old_length;
}
template <typename F>
int min_left(int r, F f) const {
assert(0 <= r && r <= old_length);
assert(f(Monoid::id()));
if (r == 0) {
return 0;
}
r += length;
Value prod = Monoid::id();
do {
--r;
while (r > 1 && (r & 1)) {
r >>= 1;
}
if (!f(Monoid::op(node[r], prod))) {
while (r < length) {
r = (r << 1) | 1;
if (f(Monoid::op(node[r], prod))) {
prod = Monoid::op(node[r--], prod);
}
}
return r + 1 - length;
}
prod = Monoid::op(prod, node[r]);
} while ((r & -r) != r);
return 0;
}
};
// ============
// ============
#include <cassert>
#include <iostream>
#include <type_traits>
// ============
#include <utility>
constexpr bool is_prime(unsigned n) {
if (n == 0 || n == 1) {
return false;
}
for (unsigned i = 2; i * i <= n; ++i) {
if (n % i == 0) {
return false;
}
}
return true;
}
constexpr unsigned mod_pow(unsigned x, unsigned y, unsigned mod) {
unsigned ret = 1, self = x;
while (y != 0) {
if (y & 1) {
ret = (unsigned)((unsigned long long)ret * self % mod);
}
self = (unsigned)((unsigned long long)self * self % mod);
y /= 2;
}
return ret;
}
template <unsigned mod>
constexpr unsigned primitive_root() {
static_assert(is_prime(mod), "`mod` must be a prime number.");
if (mod == 2) {
return 1;
}
unsigned primes[32] = {};
int it = 0;
{
unsigned m = mod - 1;
for (unsigned i = 2; i * i <= m; ++i) {
if (m % i == 0) {
primes[it++] = i;
while (m % i == 0) {
m /= i;
}
}
}
if (m != 1) {
primes[it++] = m;
}
}
for (unsigned i = 2; i < mod; ++i) {
bool ok = true;
for (int j = 0; j < it; ++j) {
if (mod_pow(i, (mod - 1) / primes[j], mod) == 1) {
ok = false;
break;
}
}
if (ok) return i;
}
return 0;
}
// y >= 1
template <typename T>
constexpr T safe_mod(T x, T y) {
x %= y;
if (x < 0) {
x += y;
}
return x;
}
// y != 0
template <typename T>
constexpr T floor_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return x / y;
} else {
return -((-x + y - 1) / y);
}
}
// y != 0
template <typename T>
constexpr T ceil_div(T x, T y) {
if (y < 0) {
x *= -1;
y *= -1;
}
if (x >= 0) {
return (x + y - 1) / y;
} else {
return -(-x / y);
}
}
// b >= 1
// returns (g, x) s.t. g = gcd(a, b), a * x = g (mod b), 0 <= x < b / g
// from ACL
template <typename T>
std::pair<T, T> extgcd(T a, T b) {
a = safe_mod(a, b);
T s = b, t = a, m0 = 0, m1 = 1;
while (t) {
T u = s / t;
s -= t * u;
m0 -= m1 * u;
std::swap(s, t);
std::swap(m0, m1);
}
if (m0 < 0) {
m0 += b / s;
}
return std::pair<T, T>(s, m0);
}
// b >= 1
// returns (g, x, y) s.t. g = gcd(a, b), a * x + b * y = g, 0 <= x < b / g, |y| < max(2, |a| / g)
template <typename T>
std::tuple<T, T, T> extgcd2(T a, T b) {
T _a = safe_mod(a, b);
T quot = (a - _a) / b;
T x00 = 0, x01 = 1, y0 = b;
T x10 = 1, x11 = -quot, y1 = _a;
while (y1) {
T u = y0 / y1;
x00 -= u * x10;
x01 -= u * x11;
y0 -= u * y1;
std::swap(x00, x10);
std::swap(x01, x11);
std::swap(y0, y1);
}
if (x00 < 0) {
x00 += b / y0;
x01 -= a / y0;
}
return std::tuple<T, T, T>(y0, x00, x01);
}
// gcd(x, m) == 1
template <typename T>
T inv_mod(T x, T m) {
return extgcd(x, m).second;
}
// ============
template <unsigned mod>
struct ModInt {
static_assert(mod != 0, "`mod` must not be equal to 0.");
static_assert(mod < (1u << 31),
"`mod` must be less than (1u << 31) = 2147483648.");
unsigned val;
static constexpr unsigned get_mod() { return mod; }
constexpr ModInt() : val(0) {}
template <typename T, std::enable_if_t<std::is_signed_v<T>> * = nullptr>
constexpr ModInt(T x)
: val((unsigned)((long long)x % (long long)mod + (x < 0 ? mod : 0))) {}
template <typename T, std::enable_if_t<std::is_unsigned_v<T>> * = nullptr>
constexpr ModInt(T x) : val((unsigned)(x % mod)) {}
static constexpr ModInt raw(unsigned x) {
ModInt<mod> ret;
ret.val = x;
return ret;
}
constexpr unsigned get_val() const { return val; }
constexpr ModInt operator+() const { return *this; }
constexpr ModInt operator-() const { return ModInt<mod>(0u) - *this; }
constexpr ModInt &operator+=(const ModInt &rhs) {
val += rhs.val;
if (val >= mod) val -= mod;
return *this;
}
constexpr ModInt &operator-=(const ModInt &rhs) {
val -= rhs.val;
if (val >= mod) val += mod;
return *this;
}
constexpr ModInt &operator*=(const ModInt &rhs) {
val = (unsigned long long)val * rhs.val % mod;
return *this;
}
constexpr ModInt &operator/=(const ModInt &rhs) {
val = (unsigned long long)val * rhs.inv().val % mod;
return *this;
}
friend constexpr ModInt operator+(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) += rhs;
}
friend constexpr ModInt operator-(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) -= rhs;
}
friend constexpr ModInt operator*(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) *= rhs;
}
friend constexpr ModInt operator/(const ModInt &lhs, const ModInt &rhs) {
return ModInt<mod>(lhs) /= rhs;
}
constexpr ModInt pow(unsigned long long x) const {
ModInt<mod> ret = ModInt<mod>::raw(1);
ModInt<mod> self = *this;
while (x != 0) {
if (x & 1) ret *= self;
self *= self;
x >>= 1;
}
return ret;
}
constexpr ModInt inv() const {
static_assert(is_prime(mod), "`mod` must be a prime number.");
assert(val != 0);
return this->pow(mod - 2);
}
friend std::istream &operator>>(std::istream &is, ModInt<mod> &x) {
long long val;
is >> val;
x.val = val % mod + (val < 0 ? mod : 0);
return is;
}
friend std::ostream &operator<<(std::ostream &os, const ModInt<mod> &x) {
os << x.val;
return os;
}
friend bool operator==(const ModInt &lhs, const ModInt &rhs) {
return lhs.val == rhs.val;
}
friend bool operator!=(const ModInt &lhs, const ModInt &rhs) {
return lhs.val != rhs.val;
}
};
template <unsigned mod>
void debug(ModInt<mod> x) {
std::cerr << x.val;
}
// ============
struct Ops {
using Value = u64;
static Value id() {
return 0;
}
static Value op(Value x, Value y) {
return x | y;
}
};
using M = ModInt<998244353>;
constexpr i32 D = 30;
u32 calc(u32 x, u32 d) {
u32 y = 0;
u32 bit_x = (x >> d) & 1;
REP(i, D) {
u32 bit = (x >> i) & 1;
if (bit ^ bit_x) {
y ^= 1u << i;
}
}
return y;
}
void solve() {
array<M, 2 * D + 1> pw;
pw[0] = M(1);
REP(i, LEN(pw) - 1) {
pw[i + 1] = pw[i] + pw[i];
}
I32(n, q);
VEC(u32, a, n);
SegmentTree<Ops> seg((D / 2 + 1) * n, [&](i32 i) -> u64 {
i32 layer = i / n;
i32 idx = i % n;
if (layer == D / 2) {
return a[idx];
}
u64 low = calc(a[idx], 2 * layer);
u64 high = calc(a[idx], 2 * layer + 1);
DBG(i, layer, idx, low, high);
return low | (high << D);
});
REP(qi, q) {
I32(ty);
if (ty == 1) {
I32(p);
U32(x);
--p;
seg.update(D / 2 * n + p, x);
REP(layer, D / 2) {
u64 low = calc(x, 2 * layer);
u64 high = calc(x, 2 * layer + 1);
seg.update(layer * n + p, low | (high << D));
}
a[p] = x;
} else {
I32(l, r);
--l;
if (r - l == 1) {
u64 val = a[l];
cout << M(val * val) << '\n';
continue;
}
array<u64, D / 2 + 1> qry;
REP(layer, D / 2 + 1) {
qry[layer] = seg.prod(layer * n + l, layer * n + r);
}
u64 tot = qry[D / 2];
DBG(tot);
M ans;
REP(d, D) {
u64 ask = qry[d / 2];
if (d % 2 == 0) {
ask &= (1u << D) - 1;
} else {
ask >>= D;
}
DBG(d, ask);
REP(e, d + 1, D) {
bool cont = (ask >> e) & 1;
if (cont) {
if (((tot >> d) & 1) && ((tot >> e) & 1)) {
ans += pw[d + e + 1];
}
} else {
if ((tot >> d) & 1) {
DBG(d, e);
ans += pw[d + e + 2];
}
}
}
if ((tot >> d) & 1) {
ans += pw[2 * d + 1];
}
}
DBG(ans);
ans *= M(2).pow(r - l - 2);
cout << ans << '\n';
}
}
}
int main() {
i32 t = 1;
// cin >> t;
while (t--) {
solve();
}
}