結果
| 問題 | No.2605 Pickup Parentheses |
| ユーザー |
 hitonanode
|
| 提出日時 | 2024-01-12 21:56:26 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 188 ms / 2,000 ms |
| コード長 | 24,739 bytes |
| コンパイル時間 | 2,736 ms |
| コンパイル使用メモリ | 219,920 KB |
| 実行使用メモリ | 20,932 KB |
| 最終ジャッジ日時 | 2024-09-30 06:22:53 |
| 合計ジャッジ時間 | 10,084 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 1 ms
6,816 KB |
| testcase_01 | AC | 2 ms
6,816 KB |
| testcase_02 | AC | 1 ms
6,816 KB |
| testcase_03 | AC | 3 ms
6,816 KB |
| testcase_04 | AC | 3 ms
6,820 KB |
| testcase_05 | AC | 4 ms
6,816 KB |
| testcase_06 | AC | 5 ms
6,820 KB |
| testcase_07 | AC | 4 ms
6,820 KB |
| testcase_08 | AC | 6 ms
6,816 KB |
| testcase_09 | AC | 2 ms
6,816 KB |
| testcase_10 | AC | 4 ms
6,820 KB |
| testcase_11 | AC | 3 ms
6,820 KB |
| testcase_12 | AC | 2 ms
6,820 KB |
| testcase_13 | AC | 4 ms
6,816 KB |
| testcase_14 | AC | 4 ms
6,816 KB |
| testcase_15 | AC | 5 ms
6,820 KB |
| testcase_16 | AC | 2 ms
6,816 KB |
| testcase_17 | AC | 5 ms
6,820 KB |
| testcase_18 | AC | 168 ms
19,104 KB |
| testcase_19 | AC | 83 ms
11,408 KB |
| testcase_20 | AC | 19 ms
6,824 KB |
| testcase_21 | AC | 11 ms
6,820 KB |
| testcase_22 | AC | 16 ms
6,816 KB |
| testcase_23 | AC | 168 ms
19,236 KB |
| testcase_24 | AC | 19 ms
6,820 KB |
| testcase_25 | AC | 180 ms
20,136 KB |
| testcase_26 | AC | 181 ms
20,172 KB |
| testcase_27 | AC | 164 ms
19,076 KB |
| testcase_28 | AC | 175 ms
20,136 KB |
| testcase_29 | AC | 39 ms
7,700 KB |
| testcase_30 | AC | 87 ms
12,052 KB |
| testcase_31 | AC | 84 ms
11,644 KB |
| testcase_32 | AC | 41 ms
7,668 KB |
| testcase_33 | AC | 177 ms
20,172 KB |
| testcase_34 | AC | 170 ms
19,756 KB |
| testcase_35 | AC | 161 ms
18,956 KB |
| testcase_36 | AC | 163 ms
19,028 KB |
| testcase_37 | AC | 173 ms
19,484 KB |
| testcase_38 | AC | 66 ms
11,804 KB |
| testcase_39 | AC | 33 ms
7,484 KB |
| testcase_40 | AC | 145 ms
18,816 KB |
| testcase_41 | AC | 143 ms
20,636 KB |
| testcase_42 | AC | 139 ms
20,512 KB |
| testcase_43 | AC | 33 ms
7,796 KB |
| testcase_44 | AC | 68 ms
11,692 KB |
| testcase_45 | AC | 33 ms
7,660 KB |
| testcase_46 | AC | 33 ms
7,436 KB |
| testcase_47 | AC | 5 ms
6,816 KB |
| testcase_48 | AC | 136 ms
20,064 KB |
| testcase_49 | AC | 139 ms
19,736 KB |
| testcase_50 | AC | 69 ms
11,952 KB |
| testcase_51 | AC | 135 ms
19,512 KB |
| testcase_52 | AC | 68 ms
12,488 KB |
| testcase_53 | AC | 137 ms
20,212 KB |
| testcase_54 | AC | 68 ms
12,264 KB |
| testcase_55 | AC | 137 ms
19,564 KB |
| testcase_56 | AC | 33 ms
7,788 KB |
| testcase_57 | AC | 137 ms
19,496 KB |
| testcase_58 | AC | 164 ms
20,336 KB |
| testcase_59 | AC | 188 ms
20,340 KB |
| testcase_60 | AC | 183 ms
20,212 KB |
| testcase_61 | AC | 179 ms
20,084 KB |
| testcase_62 | AC | 171 ms
20,212 KB |
| testcase_63 | AC | 172 ms
20,212 KB |
| testcase_64 | AC | 165 ms
20,208 KB |
| testcase_65 | AC | 185 ms
20,212 KB |
| testcase_66 | AC | 164 ms
20,212 KB |
| testcase_67 | AC | 181 ms
20,208 KB |
| testcase_68 | AC | 136 ms
20,932 KB |
| testcase_69 | AC | 1 ms
6,816 KB |
| testcase_70 | AC | 3 ms
6,816 KB |
コンパイルメッセージ
main.cpp:400:9: warning: #pragma once in main file
400 | #pragma once
| ^~~~
ソースコード
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif
#include <cassert>
#include <iostream>
#include <set>
#include <vector>
template <int md> struct ModInt {
using lint = long long;
constexpr static int mod() { return md; }
static int get_primitive_root() {
static int primitive_root = 0;
if (!primitive_root) {
primitive_root = [&]() {
std::set<int> fac;
int v = md - 1;
for (lint i = 2; i * i <= v; i++)
while (v % i == 0) fac.insert(i), v /= i;
if (v > 1) fac.insert(v);
for (int g = 1; g < md; g++) {
bool ok = true;
for (auto i : fac)
if (ModInt(g).pow((md - 1) / i) == 1) {
ok = false;
break;
}
if (ok) return g;
}
return -1;
}();
}
return primitive_root;
}
int val_;
int val() const noexcept { return val_; }
constexpr ModInt() : val_(0) {}
constexpr ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; }
constexpr ModInt(lint v) { _setval(v % md + md); }
constexpr explicit operator bool() const { return val_ != 0; }
constexpr ModInt operator+(const ModInt &x) const {
return ModInt()._setval((lint)val_ + x.val_);
}
constexpr ModInt operator-(const ModInt &x) const {
return ModInt()._setval((lint)val_ - x.val_ + md);
}
constexpr ModInt operator*(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.val_ % md);
}
constexpr ModInt operator/(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.inv().val() % md);
}
constexpr ModInt operator-() const { return ModInt()._setval(md - val_); }
constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt(a) + x; }
friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt(a) - x; }
friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt(a) * x; }
friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt(a) / x; }
constexpr bool operator==(const ModInt &x) const { return val_ == x.val_; }
constexpr bool operator!=(const ModInt &x) const { return val_ != x.val_; }
constexpr bool operator<(const ModInt &x) const {
return val_ < x.val_;
} // To use std::map<ModInt, T>
friend std::istream &operator>>(std::istream &is, ModInt &x) {
lint t;
return is >> t, x = ModInt(t), is;
}
constexpr friend std::ostream &operator<<(std::ostream &os, const ModInt &x) {
return os << x.val_;
}
constexpr ModInt pow(lint n) const {
ModInt ans = 1, tmp = *this;
while (n) {
if (n & 1) ans *= tmp;
tmp *= tmp, n >>= 1;
}
return ans;
}
static constexpr int cache_limit = std::min(md, 1 << 21);
static std::vector<ModInt> facs, facinvs, invs;
constexpr static void _precalculation(int N) {
const int l0 = facs.size();
if (N > md) N = md;
if (N <= l0) return;
facs.resize(N), facinvs.resize(N), invs.resize(N);
for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;
facinvs[N - 1] = facs.back().pow(md - 2);
for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);
for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];
}
constexpr ModInt inv() const {
if (this->val_ < cache_limit) {
if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0};
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return invs[this->val_];
} else {
return this->pow(md - 2);
}
}
constexpr ModInt fac() const {
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return facs[this->val_];
}
constexpr ModInt facinv() const {
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return facinvs[this->val_];
}
constexpr ModInt doublefac() const {
lint k = (this->val_ + 1) / 2;
return (this->val_ & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac())
: ModInt(k).fac() * ModInt(2).pow(k);
}
constexpr ModInt nCr(int r) const {
if (r < 0 or this->val_ < r) return ModInt(0);
return this->fac() * (*this - r).facinv() * ModInt(r).facinv();
}
constexpr ModInt nPr(int r) const {
if (r < 0 or this->val_ < r) return ModInt(0);
return this->fac() * (*this - r).facinv();
}
static ModInt binom(int n, int r) {
static long long bruteforce_times = 0;
if (r < 0 or n < r) return ModInt(0);
if (n <= bruteforce_times or n < (int)facs.size()) return ModInt(n).nCr(r);
r = std::min(r, n - r);
ModInt ret = ModInt(r).facinv();
for (int i = 0; i < r; ++i) ret *= n - i;
bruteforce_times += r;
return ret;
}
// Multinomial coefficient, (k_1 + k_2 + ... + k_m)! / (k_1! k_2! ... k_m!)
// Complexity: O(sum(ks))
template <class Vec> static ModInt multinomial(const Vec &ks) {
ModInt ret{1};
int sum = 0;
for (int k : ks) {
assert(k >= 0);
ret *= ModInt(k).facinv(), sum += k;
}
return ret * ModInt(sum).fac();
}
// Catalan number, C_n = binom(2n, n) / (n + 1)
// C_0 = 1, C_1 = 1, C_2 = 2, C_3 = 5, C_4 = 14, ...
// https://oeis.org/A000108
// Complexity: O(n)
static ModInt catalan(int n) {
if (n < 0) return ModInt(0);
return ModInt(n * 2).fac() * ModInt(n + 1).facinv() * ModInt(n).facinv();
}
ModInt sqrt() const {
if (val_ == 0) return 0;
if (md == 2) return val_;
if (pow((md - 1) / 2) != 1) return 0;
ModInt b = 1;
while (b.pow((md - 1) / 2) == 1) b += 1;
int e = 0, m = md - 1;
while (m % 2 == 0) m >>= 1, e++;
ModInt x = pow((m - 1) / 2), y = (*this) * x * x;
x *= (*this);
ModInt z = b.pow(m);
while (y != 1) {
int j = 0;
ModInt t = y;
while (t != 1) j++, t *= t;
z = z.pow(1LL << (e - j - 1));
x *= z, z *= z, y *= z;
e = j;
}
return ModInt(std::min(x.val_, md - x.val_));
}
};
template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};
using mint = ModInt<998244353>;
// Integer convolution for arbitrary mod
// with NTT (and Garner's algorithm) for ModInt / ModIntRuntime class.
// We skip Garner's algorithm if `skip_garner` is true or mod is in `nttprimes`.
// input: a (size: n), b (size: m)
// return: vector (size: n + m - 1)
template <typename MODINT>
std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner);
constexpr int nttprimes[3] = {998244353, 167772161, 469762049};
// Integer FFT (Fast Fourier Transform) for ModInt class
// (Also known as Number Theoretic Transform, NTT)
// is_inverse: inverse transform
// ** Input size must be 2^n **
template <typename MODINT> void ntt(std::vector<MODINT> &a, bool is_inverse = false) {
int n = a.size();
if (n == 1) return;
static const int mod = MODINT::mod();
static const MODINT root = MODINT::get_primitive_root();
assert(__builtin_popcount(n) == 1 and (mod - 1) % n == 0);
static std::vector<MODINT> w{1}, iw{1};
for (int m = w.size(); m < n / 2; m *= 2) {
MODINT dw = root.pow((mod - 1) / (4 * m)), dwinv = 1 / dw;
w.resize(m * 2), iw.resize(m * 2);
for (int i = 0; i < m; i++) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv;
}
if (!is_inverse) {
for (int m = n; m >>= 1;) {
for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
for (int i = s; i < s + m; i++) {
MODINT x = a[i], y = a[i + m] * w[k];
a[i] = x + y, a[i + m] = x - y;
}
}
}
} else {
for (int m = 1; m < n; m *= 2) {
for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
for (int i = s; i < s + m; i++) {
MODINT x = a[i], y = a[i + m];
a[i] = x + y, a[i + m] = (x - y) * iw[k];
}
}
}
int n_inv = MODINT(n).inv().val();
for (auto &v : a) v *= n_inv;
}
}
template <int MOD>
std::vector<ModInt<MOD>> nttconv_(const std::vector<int> &a, const std::vector<int> &b) {
int sz = a.size();
assert(a.size() == b.size() and __builtin_popcount(sz) == 1);
std::vector<ModInt<MOD>> ap(sz), bp(sz);
for (int i = 0; i < sz; i++) ap[i] = a[i], bp[i] = b[i];
ntt(ap, false);
if (a == b)
bp = ap;
else
ntt(bp, false);
for (int i = 0; i < sz; i++) ap[i] *= bp[i];
ntt(ap, true);
return ap;
}
long long garner_ntt_(int r0, int r1, int r2, int mod) {
using mint2 = ModInt<nttprimes[2]>;
static const long long m01 = 1LL * nttprimes[0] * nttprimes[1];
static const long long m0_inv_m1 = ModInt<nttprimes[1]>(nttprimes[0]).inv().val();
static const long long m01_inv_m2 = mint2(m01).inv().val();
int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1];
auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * m01_inv_m2;
return (r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val()) % mod;
}
template <typename MODINT>
std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner) {
if (a.empty() or b.empty()) return {};
int sz = 1, n = a.size(), m = b.size();
while (sz < n + m) sz <<= 1;
if (sz <= 16) {
std::vector<MODINT> ret(n + m - 1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) ret[i + j] += a[i] * b[j];
}
return ret;
}
int mod = MODINT::mod();
if (skip_garner or
std::find(std::begin(nttprimes), std::end(nttprimes), mod) != std::end(nttprimes)) {
a.resize(sz), b.resize(sz);
if (a == b) {
ntt(a, false);
b = a;
} else {
ntt(a, false), ntt(b, false);
}
for (int i = 0; i < sz; i++) a[i] *= b[i];
ntt(a, true);
a.resize(n + m - 1);
} else {
std::vector<int> ai(sz), bi(sz);
for (int i = 0; i < n; i++) ai[i] = a[i].val();
for (int i = 0; i < m; i++) bi[i] = b[i].val();
auto ntt0 = nttconv_<nttprimes[0]>(ai, bi);
auto ntt1 = nttconv_<nttprimes[1]>(ai, bi);
auto ntt2 = nttconv_<nttprimes[2]>(ai, bi);
a.resize(n + m - 1);
for (int i = 0; i < n + m - 1; i++)
a[i] = garner_ntt_(ntt0[i].val(), ntt1[i].val(), ntt2[i].val(), mod);
}
return a;
}
template <typename MODINT>
std::vector<MODINT> nttconv(const std::vector<MODINT> &a, const std::vector<MODINT> &b) {
return nttconv<MODINT>(a, b, false);
}
#pragma once
namespace fps_nttmod {
// Calculate the inverse of f(x) mod x^d
// f(x) * g(x) = 1 mod x^d
// If d = -1, d is set to f.size()
// Complexity: O(d log d)
template <class NTTModInt>
std::vector<NTTModInt> inv(const std::vector<NTTModInt> &f, int d = -1) {
assert(d >= -1);
const int n = f.size();
if (d == -1) d = n;
if (d == 0) return {};
assert(f.front() != NTTModInt(0));
using F = std::vector<NTTModInt>;
F res{f.front().inv()}; // f(x) g_m(x) = 1 mod x^m
for (int m = 1; m < d; m *= 2) { // g_2m = (2g_m - f g_m^2) mod x^2m
F g_m{res.cbegin(), res.cbegin() + m};
g_m.resize(2 * m);
ntt(g_m, false);
F f_{f.cbegin(), f.cbegin() + std::min(n, 2 * m)};
f_.resize(2 * m);
ntt(f_, false);
for (int i = 0; i < 2 * m; ++i) f_.at(i) *= g_m.at(i);
ntt(f_, true);
std::rotate(f_.begin(), f_.begin() + m, f_.end());
for (int i = m; i < 2 * m; ++i) f_.at(i) = 0;
ntt(f_, false);
for (int i = 0; i < 2 * m; ++i) f_.at(i) *= g_m.at(i);
ntt(f_, true);
for (int i = 0; i < m; ++i) f_.at(i) = -f_.at(i);
res.insert(res.end(), f_.begin(), f_.begin() + m);
}
res.resize(d);
return res;
}
// Calculate the integral of f(x)
// Complexity: O(len(f))
template <class NTTModInt> void integ_inplace(std::vector<NTTModInt> &f) {
if (f.empty()) return;
for (int i = (int)f.size() - 1; i > 0; --i) f.at(i) = f.at(i - 1) * NTTModInt(i).inv();
f.front() = NTTModInt(0);
}
// Calculate the derivative of f(x)
// Complexity: O(len(f))
template <class NTTModInt> void deriv_inplace(std::vector<NTTModInt> &f) {
if (f.empty()) return;
for (int i = 1; i < (int)f.size(); ++i) f.at(i - 1) = f.at(i) * i;
f.back() = NTTModInt(0);
}
// Calculate log f(x) mod x^d
// Require f(0) = 1 mod x^d
// Complexity: O(d log d)
template <class NTTModInt>
std::vector<NTTModInt> log(const std::vector<NTTModInt> &f, int d = -1) {
assert(d >= -1);
const int n = f.size();
if (d < 0) d = n;
if (d == 0) return {};
assert(f.front() == NTTModInt(1));
std::vector<NTTModInt> inv_f = inv(f, d), df{f.cbegin(), f.cbegin() + std::min(d, n)};
deriv_inplace(df);
auto ret = nttconv(inv_f, df);
ret.resize(d);
integ_inplace(ret);
return ret;
}
template <class NTTModInt>
std::vector<NTTModInt> exp(const std::vector<NTTModInt> &h, int d = -1) {
assert(d >= -1);
const int n = h.size();
if (d < 0) d = n;
if (d == 0) return {};
assert(h.empty() or h.front() == NTTModInt(0));
using F = std::vector<NTTModInt>;
F g{1}, g_fft;
std::vector<NTTModInt> ret(d);
ret.front() = 1;
auto h_deriv = h;
h_deriv.resize(d);
deriv_inplace(h_deriv);
for (int m = 1; m < d; m *= 2) {
F f_fft = ret;
f_fft.resize(m * 2);
ntt(f_fft, false);
// 2a
if (m > 1) {
F tmp{f_fft.cbegin(), f_fft.cbegin() + m};
for (int i = 0; i < m; ++i) tmp.at(i) *= g_fft.at(i);
ntt(tmp, true);
tmp.erase(tmp.begin(), tmp.begin() + m / 2);
tmp.resize(m);
ntt(tmp, false);
for (int i = 0; i < m; ++i) tmp.at(i) *= -g_fft.at(i);
ntt(tmp, true);
tmp.resize(m / 2);
g.insert(g.end(), tmp.cbegin(), tmp.cbegin() + m / 2);
}
//
F t{ret.cbegin(), ret.cbegin() + m};
deriv_inplace(t);
{
F r{h_deriv.cbegin(), h_deriv.cbegin() + m - 1};
r.resize(m);
ntt(r, false);
for (int i = 0; i < m; ++i) r.at(i) *= f_fft.at(i);
ntt(r, true);
for (int i = 0; i < m; ++i) t.at(i) -= r.at(i);
std::rotate(t.begin(), t.end() - 1, t.end());
}
//
t.resize(2 * m);
ntt(t, false);
g_fft = g;
g_fft.resize(2 * m);
ntt(g_fft, false);
for (int i = 0; i < 2 * m; ++i) t.at(i) *= g_fft.at(i);
ntt(t, true);
t.resize(m);
//
F v{h.begin() + std::min(m, n), h.begin() + std::min({d, 2 * m, n})};
v.resize(m);
t.insert(t.begin(), m - 1, 0);
t.push_back(0);
integ_inplace(t);
for (int i = 0; i < m; ++i) v.at(i) -= t.at(m + i);
//
v.resize(2 * m);
ntt(v, false);
for (int i = 0; i < 2 * m; ++i) v.at(i) *= f_fft.at(i);
ntt(v, true);
v.resize(m);
for (int i = 0; i < std::min(d - m, m); ++i) ret.at(m + i) = v.at(i);
}
return ret;
}
// Calculate f(x)^k mod x^d
// assume 0^0 = 1
template <class NTTModInt>
std::vector<NTTModInt> pow(const std::vector<NTTModInt> &A, long long k, int d = -1) {
assert(d >= -1);
const int n = A.size();
if (d < 0) d = n;
if (k == 0) {
std::vector<NTTModInt> ret{NTTModInt(1)}; // assume 0^0 = 1
ret.resize(d);
return ret;
}
int l = 0;
long long shift = 0;
while (l < (int)A.size() and A.at(l) == NTTModInt(0) and shift < d) {
++l;
shift += k;
}
if (l == (int)A.size() or shift >= d) return std::vector<NTTModInt>(d, 0);
const NTTModInt cpow = A.at(l).pow(k), cinv = A.at(l).inv();
std::vector<NTTModInt> tmp{A.cbegin() + l, A.cbegin() + std::min<int>(n, d - l * k + l)};
for (auto &x : tmp) x *= cinv;
tmp = log(tmp, d - l * k);
for (auto &x : tmp) x *= k;
tmp = exp(tmp, d - l * k);
for (auto &x : tmp) x *= cpow;
tmp.insert(tmp.begin(), l * k, NTTModInt(0));
tmp.resize(d);
return tmp;
}
} // namespace fps_nttmod
int main() {
int N, M;
cin >> N >> M;
vector<mint> f(N + 2);
vector<int> lencnt(N + 1);
REP(i, M) {
int l, r;
cin >> l >> r;
--l;
int len = r - l;
if (len % 2) continue;
lencnt.at(len)++;
dbg(len);
}
REP(l, lencnt.size()) {
if (!lencnt.at(l)) continue;
mint coeff = lencnt.at(l);
for (int j = 1; j * l <= N; ++j) {
f.at(j * l) -= mint(j).inv() * mint::catalan(l / 2).pow(j) * coeff;
// if (j % 2) {
// } else {
// f.at(j * l) -= mint(j).inv() * coeff;
// }
}
}
f = fps_nttmod::exp(f);
dbg(f);
mint ret = 0;
REP(l, N + 1) {
if (l % 2) continue;
if ((N - l) % 2) continue;
ret += f.at(l) * mint::catalan((N - l) / 2);
}
cout << ret << '\n';
}