結果
| 問題 | No.2605 Pickup Parentheses |
| ユーザー |
 noya2
|
| 提出日時 | 2024-01-17 16:29:27 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 166 ms / 2,000 ms |
| コード長 | 29,307 bytes |
| コンパイル時間 | 3,630 ms |
| コンパイル使用メモリ | 270,124 KB |
| 実行使用メモリ | 11,264 KB |
| 最終ジャッジ日時 | 2024-03-20 19:53:50 |
| 合計ジャッジ時間 | 8,033 ms |
|
ジャッジサーバーID （参考情報） |
judge15 / judge11 |
（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 | 7 ms
6,548 KB |
| testcase_01 | AC | 7 ms
6,548 KB |
| testcase_02 | AC | 7 ms
6,548 KB |
| testcase_03 | AC | 7 ms
6,548 KB |
| testcase_04 | AC | 8 ms
6,548 KB |
| testcase_05 | AC | 7 ms
6,548 KB |
| testcase_06 | AC | 8 ms
6,548 KB |
| testcase_07 | AC | 8 ms
6,548 KB |
| testcase_08 | AC | 8 ms
6,548 KB |
| testcase_09 | AC | 7 ms
6,548 KB |
| testcase_10 | AC | 7 ms
6,548 KB |
| testcase_11 | AC | 7 ms
6,548 KB |
| testcase_12 | AC | 7 ms
6,548 KB |
| testcase_13 | AC | 7 ms
6,548 KB |
| testcase_14 | AC | 7 ms
6,548 KB |
| testcase_15 | AC | 7 ms
6,548 KB |
| testcase_16 | AC | 7 ms
6,548 KB |
| testcase_17 | AC | 7 ms
6,548 KB |
| testcase_18 | AC | 90 ms
7,980 KB |
| testcase_19 | AC | 46 ms
6,884 KB |
| testcase_20 | AC | 14 ms
6,548 KB |
| testcase_21 | AC | 10 ms
6,548 KB |
| testcase_22 | AC | 8 ms
6,548 KB |
| testcase_23 | AC | 90 ms
7,612 KB |
| testcase_24 | AC | 13 ms
6,548 KB |
| testcase_25 | AC | 113 ms
8,216 KB |
| testcase_26 | AC | 117 ms
8,060 KB |
| testcase_27 | AC | 77 ms
7,588 KB |
| testcase_28 | AC | 11 ms
6,548 KB |
| testcase_29 | AC | 15 ms
6,548 KB |
| testcase_30 | AC | 29 ms
6,548 KB |
| testcase_31 | AC | 9 ms
6,548 KB |
| testcase_32 | AC | 7 ms
6,548 KB |
| testcase_33 | AC | 58 ms
7,092 KB |
| testcase_34 | AC | 11 ms
6,548 KB |
| testcase_35 | AC | 8 ms
6,548 KB |
| testcase_36 | AC | 10 ms
6,548 KB |
| testcase_37 | AC | 52 ms
6,812 KB |
| testcase_38 | AC | 26 ms
6,548 KB |
| testcase_39 | AC | 13 ms
6,548 KB |
| testcase_40 | AC | 58 ms
7,500 KB |
| testcase_41 | AC | 55 ms
7,136 KB |
| testcase_42 | AC | 78 ms
7,748 KB |
| testcase_43 | AC | 18 ms
6,548 KB |
| testcase_44 | AC | 17 ms
6,548 KB |
| testcase_45 | AC | 7 ms
6,548 KB |
| testcase_46 | AC | 10 ms
6,548 KB |
| testcase_47 | AC | 6 ms
6,548 KB |
| testcase_48 | AC | 7 ms
6,548 KB |
| testcase_49 | AC | 45 ms
6,912 KB |
| testcase_50 | AC | 19 ms
6,548 KB |
| testcase_51 | AC | 7 ms
6,548 KB |
| testcase_52 | AC | 28 ms
6,548 KB |
| testcase_53 | AC | 36 ms
6,588 KB |
| testcase_54 | AC | 22 ms
6,548 KB |
| testcase_55 | AC | 30 ms
6,548 KB |
| testcase_56 | AC | 11 ms
6,548 KB |
| testcase_57 | AC | 7 ms
6,548 KB |
| testcase_58 | AC | 166 ms
11,264 KB |
| testcase_59 | AC | 97 ms
8,432 KB |
| testcase_60 | AC | 117 ms
8,224 KB |
| testcase_61 | AC | 103 ms
8,324 KB |
| testcase_62 | AC | 116 ms
8,244 KB |
| testcase_63 | AC | 105 ms
8,492 KB |
| testcase_64 | AC | 115 ms
8,716 KB |
| testcase_65 | AC | 101 ms
7,668 KB |
| testcase_66 | AC | 159 ms
9,728 KB |
| testcase_67 | AC | 105 ms
7,944 KB |
| testcase_68 | AC | 7 ms
6,548 KB |
| testcase_69 | AC | 7 ms
6,548 KB |
| testcase_70 | AC | 7 ms
6,548 KB |
ソースコード
#line 2 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
using namespace std;
#include<bits/stdc++.h>
#line 1 "/Users/noya2/Desktop/Noya2_library/template/inout_old.hpp"
namespace noya2 {
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;
}
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...);
}
template<typename T>
void out(const vector<vector<T>> &vv){
int s = (int)vv.size();
for (int i = 0; i < s; i++) out(vv[i]);
}
struct IoSetup {
IoSetup(){
cin.tie(nullptr);
ios::sync_with_stdio(false);
cout << fixed << setprecision(15);
cerr << fixed << setprecision(7);
}
} iosetup_noya2;
} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/const.hpp"
namespace noya2{
const int iinf = 1'000'000'007;
const long long linf = 2'000'000'000'000'000'000LL;
const long long mod998 = 998244353;
const long long mod107 = 1000000007;
const long double pi = 3.14159265358979323;
const vector<int> dx = {0,1,0,-1,1,1,-1,-1};
const vector<int> dy = {1,0,-1,0,1,-1,-1,1};
const string ALP = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string alp = "abcdefghijklmnopqrstuvwxyz";
const string NUM = "0123456789";
void yes(){ cout << "Yes\n"; }
void no(){ cout << "No\n"; }
void YES(){ cout << "YES\n"; }
void NO(){ cout << "NO\n"; }
void yn(bool t){ t ? yes() : no(); }
void YN(bool t){ t ? YES() : NO(); }
} // namespace noya2
#line 1 "/Users/noya2/Desktop/Noya2_library/template/utils.hpp"
namespace noya2{
unsigned long long inner_binary_gcd(unsigned long long a, unsigned long long b){
if (a == 0 || b == 0) return a + b;
int n = __builtin_ctzll(a); a >>= n;
int m = __builtin_ctzll(b); b >>= m;
while (a != b) {
int mm = __builtin_ctzll(a - b);
bool f = a > b;
unsigned long long c = f ? a : b;
b = f ? b : a;
a = (c - b) >> mm;
}
return a << min(n, m);
}
template<typename T> T gcd_fast(T a, T b){ return static_cast<T>(inner_binary_gcd(abs(a),abs(b))); }
long long sqrt_fast(long long n) {
if (n <= 0) return 0;
long long x = sqrt(n);
while ((x + 1) * (x + 1) <= n) x++;
while (x * x > n) x--;
return x;
}
template<typename T> T floor_div(const T n, const T d) {
assert(d != 0);
return n / d - static_cast<T>((n ^ d) < 0 && n % d != 0);
}
template<typename T> T ceil_div(const T n, const T d) {
assert(d != 0);
return n / d + static_cast<T>((n ^ d) >= 0 && n % d != 0);
}
template<typename T> void uniq(vector<T> &v){
sort(v.begin(),v.end());
v.erase(unique(v.begin(),v.end()),v.end());
}
template <typename T, typename U> inline bool chmin(T &x, U y) { return (y < x) ? (x = y, true) : false; }
template <typename T, typename U> inline bool chmax(T &x, U y) { return (x < y) ? (x = y, true) : false; }
template<typename T> inline bool range(T l, T x, T r){ return l <= x && x < r; }
} // namespace noya2
#line 8 "/Users/noya2/Desktop/Noya2_library/template/template.hpp"
#define rep(i,n) for (int i = 0; i < (int)(n); i++)
#define repp(i,m,n) for (int i = (m); i < (int)(n); i++)
#define reb(i,n) for (int i = (int)(n-1); i >= 0; i--)
#define all(v) (v).begin(),(v).end()
using ll = long long;
using ld = long double;
using uint = unsigned int;
using ull = unsigned long long;
using pii = pair<int,int>;
using pll = pair<ll,ll>;
using pil = pair<int,ll>;
using pli = pair<ll,int>;
namespace noya2{
/* ~ (. _________ . /) */
}
using namespace noya2;
#line 2 "c.cpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/fps/fps_ntt.hpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/fps/formal_power_series.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/fps/formal_power_series.hpp"
namespace noya2{
template<typename T>
concept Field = requires (T a, T b){
a + b; a - b; a / b; a * b;
T(0); T(1);
};
template<class Info>
concept Fps_Info = requires {
typename Info::value_type;
requires Field<typename Info::value_type>;
{Info::multiply(declval<vector<typename Info::value_type>>(),declval<vector<typename Info::value_type>>())} -> convertible_to<vector<typename Info::value_type>>;
{Info::inv(declval<vector<typename Info::value_type>>(),declval<int>())} -> convertible_to<vector<typename Info::value_type>>;
{Info::integral(declval<vector<typename Info::value_type>>())} -> convertible_to<vector<typename Info::value_type>>;
};
template<Fps_Info Info>
struct FormalPowerSeries : vector<typename Info::value_type> {
using T = typename Info::value_type;
using vector<T>::vector;
using vector<T>::operator=;
using FPS = FormalPowerSeries;
FormalPowerSeries (const vector<T> &init_ = {}){ (*this) = init_; }
void shrink(){ while (!(*this).empty() && (*this).back() == T(0)) (*this).pop_back(); }
FPS &operator+=(const T &r){
if ((*this).empty()) (*this).resize(1);
(*this)[0] += r;
return *this;
}
FPS &operator-=(const T &r){
if ((*this).empty()) (*this).resize(1);
(*this)[0] -= r;
return *this;
}
FPS &operator*=(const T &r){
for (auto &x : *this) x *= r;
return *this;
}
FPS &operator/=(const T &r){
(*this) *= T(1)/r;
return *this;
}
FPS &operator<<=(const int &d){
(*this).insert((*this).begin(),d,T(0));
return *this;
}
FPS &operator>>=(const int &d){
if ((int)(*this).size() <= d) (*this).clear();
else (*this).erase((*this).begin(),(*this).begin()+d);
return *this;
}
FPS &operator+=(const FPS &r){
if ((*this).size() < r.size()) (*this).resize(r.size());
for (int i = 0; i < (int)(r.size()); i++) (*this)[i] += r[i];
return *this;
}
FPS &operator-=(const FPS &r){
if ((*this).size() < r.size()) (*this).resize(r.size());
for (int i = 0; i < (int)(r.size()); i++) (*this)[i] -= r[i];
return *this;
}
FPS &operator*=(const FPS &r){
if ((*this).empty() || r.empty()){
(*this).clear();
return *this;
}
(*this) = Info::multiply(*this,r);
return *this;
}
FPS operator+(const T &r) const { return FPS(*this) += r; }
FPS operator-(const T &r) const { return FPS(*this) -= r; }
FPS operator*(const T &r) const { return FPS(*this) *= r; }
FPS operator/(const T &r) const { return FPS(*this) /= r; }
FPS operator<<(const int &d) const { return FPS(*this) <<= d; }
FPS operator>>(const int &d) const { return FPS(*this) >>= d; }
FPS operator+(const FPS &r) const { return FPS(*this) += r; }
FPS operator-(const FPS &r) const { return FPS(*this) -= r; }
FPS operator*(const FPS &r) const { return FPS(*this) *= r; }
FPS operator+() const { return *this; }
FPS operator-() const {
FPS res(*this);
for (auto &x : res) x = -x;
return res;
}
T eval(const T &x) const {
T res = T(0), w = T(1);
for (auto &e : *this) res += e * w, w *= x;
return res;
}
static FPS dot(const FPS &lhs, const FPS &rhs){
FPS res(min(lhs.size(),rhs.size()));
for (int i = 0; i < (int)res.size(); i++) res[i] = lhs[i] * rhs[i];
return res;
}
FPS pre(int siz) const {
FPS ret((*this).begin(), (*this).begin() + min((int)this->size(), siz));
if ((int)ret.size() < siz) ret.resize(siz);
return ret;
}
FPS rev() const {
FPS ret(*this);
reverse(ret.begin(), ret.end());
return ret;
}
FPS diff() const {
const int n = (int)this->size();
FPS ret(max(0, n - 1));
T one(1), coeff(1);
for (int i = 1; i < n; i++) {
ret[i - 1] = (*this)[i] * coeff;
coeff += one;
}
return ret;
}
FPS integral() const {
FPS ret = Info::integral(*this);
return ret;
}
FPS inv(int d = -1) const {
FPS ret = Info::inv(*this,d);
return ret;
}
FPS exp(int d = -1) const {
const int n = (*this).size();
if (d == -1) d = n;
FPS f = {T(1)+(*this)[0],(*this)[1]}, res = {1,(n > 1 ? (*this)[1] : 0)};
for (int sz = 2; sz < d; sz <<= 1){
f.insert(f.end(),(*this).begin()+min(n,sz),(*this).begin()+min(n,sz*2));
if ((int)f.size() < sz*2) f.resize(sz*2);
res = res * (f - res.log(2*sz));
res.resize(sz*2);
}
res.resize(d);
return res;
}
FPS log(int d = -1) const {
assert(!(*this).empty() && (*this)[0] == T(1));
if (d == -1) d = (*this).size();
return (this->diff() * this->inv(d)).pre(d - 1).integral();
}
};
} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/math/binomial.hpp"
namespace noya2 {
template<typename mint>
struct binomial {
binomial(int len = 300000){ extend(len); }
static mint fact(int n){
if (n < 0) return 0;
while (n >= (int)_fact.size()) extend();
return _fact[n];
}
static mint ifact(int n){
if (n < 0) return 0;
while (n >= (int)_fact.size()) extend();
return _ifact[n];
}
static mint inv(int n){
return ifact(n) * fact(n-1);
}
static mint C(int n, int r){
if (!(0 <= r && r <= n)) return 0;
return fact(n) * ifact(r) * ifact(n-r);
}
static mint P(int n, int r){
if (!(0 <= r && r <= n)) return 0;
return fact(n) * ifact(n-r);
}
inline mint operator()(int n, int r) { return C(n, r); }
template<class... Cnts> static mint M(const Cnts&... cnts){
return multinomial(0,1,cnts...);
}
private:
static mint multinomial(const int& sum, const mint& div_prod){
if (sum < 0) return 0;
return fact(sum) * div_prod;
}
template<class... Tail> static mint multinomial(const int& sum, const mint& div_prod, const int& n1, const Tail&... tail){
if (n1 < 0) return 0;
return multinomial(sum+n1,div_prod*ifact(n1),tail...);
}
static vector<mint> _fact, _ifact;
static void extend(int len = -1){
if (_fact.empty()){
_fact = _ifact = {1,1};
}
int siz = _fact.size();
if (len == -1) len = siz * 2;
len = min<int>(len, mint::mod()-1);
if (len < siz) return ;
_fact.resize(len+1), _ifact.resize(len+1);
for (int i = siz; i <= len; i++) _fact[i] = _fact[i-1] * i;
_ifact[len] = _fact[len].inv();
for (int i = len; i > siz; i--) _ifact[i-1] = _ifact[i] * i;
}
};
template<typename T>
std::vector<T>binomial<T>::_fact = vector<T>(2,T(1));
template<typename T>
std::vector<T>binomial<T>::_ifact = vector<T>(2,T(1));
} // namespace noya2
#line 2 "/Users/noya2/Desktop/Noya2_library/fps/ntt.hpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"
#line 2 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"
#line 4 "/Users/noya2/Desktop/Noya2_library/math/prime.hpp"
namespace noya2 {
constexpr ll safe_mod(ll x, ll m) {
x %= m;
if (x < 0) x += m;
return x;
}
constexpr ll pow_mod_constexpr(ll x, ll n, int m) {
if (m == 1) return 0;
uint _m = (uint)(m);
ull r = 1;
ull y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
ll d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr ll bases[3] = {2, 7, 61};
for (ll a : bases) {
ll t = d;
ll y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime_flag = is_prime_constexpr(n);
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u;
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (ll)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root_flag = primitive_root_constexpr(m);
} // namespace noya2
#line 4 "/Users/noya2/Desktop/Noya2_library/utility/modint.hpp"
namespace noya2{
struct barrett {
uint _m;
ull im;
explicit barrett(uint m) : _m(m), im((ull)(-1) / m + 1) {}
uint umod() const { return _m; }
uint mul(uint a, uint b) const {
ull z = a;
z *= b;
ull x = ull((__uint128_t(z) * im) >> 64);
uint v = (uint)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
template <int m>
struct static_modint {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
constexpr static_modint() : _v(0) {}
template<signed_integral T>
constexpr static_modint(T v){
ll x = (ll)(v % (ll)(umod()));
if (x < 0) x += umod();
_v = (uint)(x);
}
template<unsigned_integral T>
constexpr static_modint(T v){
_v = (uint)(v % umod());
}
constexpr unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
constexpr mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
constexpr mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
constexpr mint& operator*=(const mint& rhs) {
ull z = _v;
z *= rhs._v;
_v = (uint)(z % umod());
return *this;
}
constexpr mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
constexpr mint operator+() const { return *this; }
constexpr mint operator-() const { return mint() - *this; }
constexpr mint pow(ll n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
constexpr mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend constexpr mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend constexpr mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend constexpr mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend constexpr mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend constexpr bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend constexpr bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
friend std::ostream &operator<<(std::ostream &os, const mint& p) {
return os << p.val();
}
friend std::istream &operator>>(std::istream &is, mint &a) {
long long t; is >> t;
a = mint(t);
return (is);
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = is_prime_flag<m>;
};
template <int id> struct dynamic_modint {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template<signed_integral T>
dynamic_modint(T v){
ll x = (ll)(v % (ll)(mod()));
if (x < 0) x += mod();
_v = (uint)(x);
}
template<unsigned_integral T>
dynamic_modint(T v){
_v = (uint)(v % mod());
}
uint val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = noya2::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
friend std::ostream &operator<<(std::ostream &os, const mint& p) {
return os << p.val();
}
friend std::istream &operator>>(std::istream &is, mint &a) {
long long t; is >> t;
a = mint(t);
return (is);
}
private:
unsigned int _v;
static barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> noya2::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
template<typename T>
concept Modint = requires (T &a){
T::mod();
a.inv();
a.val();
a.pow(declval<int>());
};
} // namespace noya2
#line 5 "/Users/noya2/Desktop/Noya2_library/fps/ntt.hpp"
namespace noya2{
template<Modint mint>
struct NTT {
static constexpr uint mod = mint::mod();
static constexpr ull mod2 = (ull)mod * mod;
static constexpr uint pr = primitive_root_constexpr(mod);
static constexpr int level = countr_zero(mod-1);
mint wp[level+1], wm[level+1];
void set_ws(){
mint r = mint(pr).pow((mod-1) >> level);
wp[level] = r, wm[level] = r.inv();
for (int i = level-1; i >= 0; i--){
wp[i] = wp[i+1] * wp[i+1];
wm[i] = wm[i+1] * wm[i+1];
}
}
NTT () { set_ws(); }
void fft4(vector<mint> &a, int k, int s = 0){
uint im = wm[2].val();
uint n = 1<<k;
uint len = n;
int l = k;
while (len > 1){
if (l == 1){
for (int i = 0; i < (1<<(k-1)); i++){
int i0 = s + i*2, i1 = i0+1;
a[i0] += a[i1];
a[i1] = a[i0] - a[i1] * 2;
}
len >>= 1;
l -= 1;
}
else {
int len4 = len/4;
int nlen = n/len;
ull r1 = 1, r2 = 1, r3 = 1, imr1 = im, imr3 = im;
for (int i = 0; i < len4; i++){
int offset = 0;
for (int j = 0; j < nlen; j++){
int i0 = s + i + offset, i1 = i0 + len4, i2 = i1 + len4, i3 = i2 + len4;
uint a0 = a[i0].val();
uint a1 = a[i1].val();
uint a2 = a[i2].val();
uint a3 = a[i3].val();
uint a0p2 = a0 + a2;
uint a1p3 = a1 + a3;
ull b0m2 = (a0 + mod - a2) * r1;
ull b1m3 = (a1 + mod - a3) * imr1;
ull c0m2 = (a0 + mod - a2) * r3;
ull c1m3 = (a1 + mod - a3) * imr3;
a[i0] = a0p2 + a1p3;
a[i1] = b0m2 + b1m3;
a[i2] = (a0p2 + mod*2 - a1p3) * r2;
a[i3] = c0m2 + mod2*2 - c1m3;
offset += len;
}
r1 = r1 * wm[l].val() % mod;
r2 = r1 * r1 % mod;
r3 = r1 * r2 % mod;
imr1 = im * r1 % mod;
imr3 = im * r3 % mod;
}
len >>= 2;
l -= 2;
}
}
}
void ifft4(vector<mint> &a, int k, int s = 0){
uint im = wp[2].val();
uint n = 1<<k;
uint len = (k & 1 ? 2 : 4);
int l = (k & 1 ? 1 : 2);
while (len <= n){
if (l == 1){
for (int i = 0; i < (1<<(k-1)); i++){
int i0 = s + i*2, i1 = i0+1;
a[i0] += a[i1];
a[i1] = a[i0] - a[i1] * 2;
}
len <<= 2;
l += 2;
}
else {
int len4 = len/4;
int nlen = n/len;
ull r1 = 1, r2 = 1, r3 = 1, imr1 = im, imr3 = im;
for (int i = 0; i < len4; i++){
int offset = 0;
for (int j = 0; j < nlen; j++){
int i0 = s + i + offset, i1 = i0 + len4, i2 = i1 + len4, i3 = i2 + len4;
ull a0 = a[i0].val();
ull a1 = a[i1].val() * r1;
ull a2 = a[i2].val() * r2;
ull a3 = a[i3].val() * r3;
ull b1 = a[i1].val() * imr1;
ull b3 = a[i3].val() * imr3;
ull a0p2 = a0 + a2;
ull a1p3 = a1 + a3;
ull a0m2 = a0 + mod2 - a2;
ull b1m3 = b1 + mod2 - b3;
a[i0] = a0p2 + a1p3;
a[i1] = a0m2 + b1m3;
a[i2] = a0p2 + mod2*2 - a1p3;
a[i3] = a0m2 + mod2*2 - b1m3;
offset += len;
}
r1 = r1 * wp[l].val() % mod;
r2 = r1 * r1 % mod;
r3 = r1 * r2 % mod;
imr1 = im * r1 % mod;
imr3 = im * r3 % mod;
}
len <<= 2;
l += 2;
}
}
}
void ntt(vector<mint> &a) {
if ((int)a.size() <= 1) return;
fft4(a, 63-countl_zero(a.size()));
}
void intt(vector<mint> &a, bool stop = false) {
if ((int)a.size() <= 1) return;
ifft4(a, 63-countl_zero(a.size()));
if (stop) return ;
mint iv = mint(a.size()).inv();
for (auto &x : a) x *= iv;
}
vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {
int l = a.size() + b.size() - 1;
if (min<int>(a.size(), b.size()) <= 40){
vector<mint> s(l);
for (int i = 0; i < (int)a.size(); i++) for (int j = 0; j < (int)b.size(); j++) s[i + j] += a[i] * b[j];
return s;
}
int k = 2, M = 4;
while (M < l) M <<= 1, ++k;
set_ws();
vector<mint> s(M);
for (int i = 0; i < (int)a.size(); ++i) s[i] = a[i];
fft4(s, k);
if (a.size() == b.size() && a == b) {
for (int i = 0; i < M; ++i) s[i] *= s[i];
}
else {
vector<mint> t(M);
for (int i = 0; i < (int)b.size(); ++i) t[i] = b[i];
fft4(t, k);
for (int i = 0; i < M; ++i) s[i] *= t[i];
}
ifft4(s, k);
s.resize(l);
mint invm = mint(M).inv();
for (int i = 0; i < l; ++i) s[i] *= invm;
return s;
}
};
} // namespace noya2
#line 6 "/Users/noya2/Desktop/Noya2_library/fps/fps_ntt.hpp"
namespace noya2{
template<typename T>
struct fps_ntt{
using value_type = T;
static NTT<T> ntt;
static vector<T> multiply(const vector<T> &a, const vector<T> &b){
return ntt.multiply(a,b);
}
static vector<T> inv(const vector<T> &a, int d = -1){
const int n = a.size();
if (d == -1) d = n;
vector<T> res = {a[0].inv()};
for (int siz = 1; siz < d; siz <<= 1){
vector<T> f(a.begin(),a.begin()+min(n,siz*2)), g(res);
f.resize(siz*2), g.resize(siz*2);
ntt.ntt(f), ntt.ntt(g);
for (int i = 0; i < siz*2; i++) f[i] *= g[i];
ntt.intt(f,true);
f.erase(f.begin(),f.begin()+siz);
f.resize(siz*2);
ntt.ntt(f);
for (int i = 0; i < siz*2; i++) f[i] *= g[i];
ntt.intt(f,true);
T siz2_inv = T(siz*2).inv(); siz2_inv *= -siz2_inv;
for (int i = 0; i < siz; i++) f[i] *= siz2_inv;
res.insert(res.end(),f.begin(),f.begin()+siz);
}
res.resize(d);
return res;
}
static binomial<T> bnm;
static vector<T> integral(const vector<T> &a){
const int n = a.size();
vector<T> res(n+1);
for (int i = 1; i <= n; i++) res[i] = a[i-1] * bnm.inv(i);
return res;
}
};
template<typename T> NTT<T> fps_ntt<T>::ntt;
template<typename T> using FPS_ntt = FormalPowerSeries<fps_ntt<T>>;
} // namespace noya2
#line 4 "c.cpp"
using mint = modint998244353;
using fps = FPS_ntt<mint>;
void solve(){
int n, m; in(n,m);
binomial<mint> bnm;
auto calc = [&](int c){
return bnm(2*c,c) * bnm.inv(c+1);
};
queue<fps> que;
rep(i,m){
int l, r; in(l,r);
int sz = r - l + 1;
if (sz % 2 == 0){
sz /= 2;
fps f(sz+1);
f[0] = 1;
f[sz] = -calc(sz);
que.push(f);
}
}
if (n % 2 == 1){
out(0);
return ;
}
if (que.empty()){
mint ans = calc(n/2);
out(ans);
return ;
}
while ((int)(que.size()) >= 2){
auto f = que.front(); que.pop();
auto g = que.front(); que.pop();
que.push(f*g);
}
auto f = que.front();
int sz = f.size();
mint ans = 0;
rep(i,sz){
ans += calc(n/2-i) * f[i];
}
out(ans);
}
int main(){
int t = 1; //in(t);
while (t--) { solve(); }
}