結果
問題 | No.2327 Inversion Sum |
ユーザー |
|
提出日時 | 2023-05-28 14:12:45 |
言語 | C++17(gcc12) (gcc 12.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 96 ms / 2,000 ms |
コード長 | 55,952 bytes |
コンパイル時間 | 27,690 ms |
コンパイル使用メモリ | 398,804 KB |
最終ジャッジ日時 | 2025-02-13 11:05:30 |
ジャッジサーバーID (参考情報) |
judge1 / judge5 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 30 |
ソースコード
#pragma region Macros#ifdef noimi#include "my_template.hpp"#else#pragma GCC target("avx2")#pragma GCC optimize("O3")#pragma GCC optimize("unroll-loops")#include <immintrin.h>#include <algorithm>#include <array>#include <bitset>#include <cassert>#include <cctype>#include <cfenv>#include <cfloat>#include <chrono>#include <cinttypes>#include <climits>#include <cmath>#include <complex>#include <cstdarg>#include <cstddef>#include <cstdint>#include <cstdio>#include <cstdlib>#include <cstring>#include <deque>#include <fstream>#include <functional>#include <immintrin.h>#include <initializer_list>#include <iomanip>#include <ios>#include <iostream>#include <istream>#include <iterator>#include <limits>#include <list>#include <map>#include <memory>#include <new>#include <numeric>#include <ostream>#include <queue>#include <random>#include <set>#include <sstream>#include <stack>#include <streambuf>#include <string>#include <tuple>#include <type_traits>#include <variant>#ifdef noimi#define oj_local(a, b) b#else#define oj_local(a, b) a#endif#define LOCAL if(oj_local(0, 1))#define OJ if(oj_local(1, 0))using namespace std;using ll = long long;using ull = unsigned long long int;using i128 = __int128_t;using pii = pair<int, int>;using pll = pair<ll, ll>;using ld = long double;template <typename T> using vc = vector<T>;template <typename T> using vvc = vector<vc<T>>;template <typename T> using vvvc = vector<vvc<T>>;using vi = vc<int>;using vl = vc<ll>;using vpi = vc<pii>;using vpl = vc<pll>;template <class T> using pq = priority_queue<T>;template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;template <typename T> int si(const T &x) { return x.size(); }template <class T, class S> inline bool chmax(T &a, const S &b) { return (a < b ? a = b, 1 : 0); }template <class T, class S> inline bool chmin(T &a, const S &b) { return (a > b ? a = b, 1 : 0); }vi iota(int n) {vi a(n);return iota(a.begin(), a.end(), 0), a;}template <typename T> vi iota(const vector<T> &a, bool greater = false) {vi res(a.size());iota(res.begin(), res.end(), 0);sort(res.begin(), res.end(), [&](int i, int j) {if(greater) return a[i] > a[j];return a[i] < a[j];});return res;}// macros#define overload5(a, b, c, d, e, name, ...) name#define overload4(a, b, c, d, name, ...) name#define endl '\n'#define REP0(n) for(ll jidlsjf = 0; jidlsjf < n; ++jidlsjf)#define REP1(i, n) for(ll i = 0; i < (n); ++i)#define REP2(i, a, b) for(ll i = (a); i < (b); ++i)#define REP3(i, a, b, c) for(ll i = (a); i < (b); i += (c))#define rep(...) overload4(__VA_ARGS__, REP3, REP2, REP1, REP0)(__VA_ARGS__)#define per0(n) for(int jidlsjf = 0; jidlsjf < (n); ++jidlsjf)#define per1(i, n) for(ll i = (n)-1; i >= 0; --i)#define per2(i, a, b) for(ll i = (a)-1; i >= b; --i)#define per3(i, a, b, c) for(ll i = (a)-1; i >= (b); i -= (c))#define per(...) overload4(__VA_ARGS__, per3, per2, per1, per0)(__VA_ARGS__)#define fore0(a) rep(a.size())#define fore1(i, a) for(auto &&i : a)#define fore2(a, b, v) for(auto &&[a, b] : v)#define fore3(a, b, c, v) for(auto &&[a, b, c] : v)#define fore4(a, b, c, d, v) for(auto &&[a, b, c, d] : v)#define fore(...) overload5(__VA_ARGS__, fore4, fore3, fore2, fore1, fore0)(__VA_ARGS__)#define setbits(j, n) for(ll iiiii = (n), j = lowbit(iiiii); iiiii; iiiii ^= 1 << j, j = lowbit(iiiii))#define perm(v) for(bool permrepflag = true; (permrepflag ? exchange(permrepflag, false) : next_permutation(all(v)));)#define fi first#define se second#define pb push_back#define ppb pop_back#define ppf pop_front#define eb emplace_back#define drop(s) cout << #s << endl, exit(0)#define si(c) (int)(c).size()#define lb(c, x) distance((c).begin(), lower_bound(all(c), (x)))#define lbg(c, x) distance((c).begin(), lower_bound(all(c), (x), greater{}))#define ub(c, x) distance((c).begin(), upper_bound(all(c), (x)))#define ubg(c, x) distance((c).begin(), upper_bound(all(c), (x), greater{}))#define rng(v, l, r) v.begin() + (l), v.begin() + (r)#define all(c) begin(c), end(c)#define rall(c) rbegin(c), rend(c)#define SORT(v) sort(all(v))#define REV(v) reverse(all(v))#define UNIQUE(x) SORT(x), x.erase(unique(all(x)), x.end())template <typename T = ll, typename S> T SUM(const S &v) { return accumulate(all(v), T(0)); }#define MIN(v) *min_element(all(v))#define MAX(v) *max_element(all(v))#define overload2(_1, _2, name, ...) name#define vec(type, name, ...) vector<type> name(__VA_ARGS__)#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))#define vvvv(type, name, a, b, c, ...)\vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))constexpr pii dx4[4] = {pii{1, 0}, pii{0, 1}, pii{-1, 0}, pii{0, -1}};constexpr pii dx8[8] = {{1, 0}, {1, 1}, {0, 1}, {-1, 1}, {-1, 0}, {-1, -1}, {0, -1}, {1, -1}};namespace yesno_impl {const string YESNO[2] = {"NO", "YES"};const string YesNo[2] = {"No", "Yes"};const string yesno[2] = {"no", "yes"};const string firstsecond[2] = {"second", "first"};const string FirstSecond[2] = {"Second", "First"};const string possiblestr[2] = {"impossible", "possible"};const string Possiblestr[2] = {"Impossible", "Possible"};void YES(bool t = 1) { cout << YESNO[t] << endl; }void NO(bool t = 1) { YES(!t); }void Yes(bool t = 1) { cout << YesNo[t] << endl; }void No(bool t = 1) { Yes(!t); }void yes(bool t = 1) { cout << yesno[t] << endl; }void no(bool t = 1) { yes(!t); }void first(bool t = 1) { cout << firstsecond[t] << endl; }void First(bool t = 1) { cout << FirstSecond[t] << endl; }void possible(bool t = 1) { cout << possiblestr[t] << endl; }void Possible(bool t = 1) { cout << Possiblestr[t] << endl; }}; // namespace yesno_implusing namespace yesno_impl;#define INT(...)\int __VA_ARGS__;\IN(__VA_ARGS__)#define INTd(...)\int __VA_ARGS__;\IN2(__VA_ARGS__)#define LL(...)\ll __VA_ARGS__;\IN(__VA_ARGS__)#define LLd(...)\ll __VA_ARGS__;\IN2(__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 VEC(type, name, size)\vector<type> name(size);\IN(name)#define VECd(type, name, size)\vector<type> name(size);\IN2(name)#define VEC2(type, name1, name2, size)\vector<type> name1(size), name2(size);\for(int i = 0; i < size; i++) IN(name1[i], name2[i])#define VEC2d(type, name1, name2, size)\vector<type> name1(size), name2(size);\for(int i = 0; i < size; i++) IN2(name1[i], name2[i])#define VEC3(type, name1, name2, name3, size)\vector<type> name1(size), name2(size), name3(size);\for(int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i])#define VEC3d(type, name1, name2, name3, size)\vector<type> name1(size), name2(size), name3(size);\for(int i = 0; i < size; i++) IN2(name1[i], name2[i], name3[i])#define VEC4(type, name1, name2, name3, name4, size)\vector<type> name1(size), name2(size), name3(size), name4(size);\for(int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i], name4[i]);#define VEC4d(type, name1, name2, name3, name4, size)\vector<type> name1(size), name2(size), name3(size), name4(size);\for(int i = 0; i < size; i++) IN2(name1[i], name2[i], name3[i], name4[i]);#define VV(type, name, h, w)\vector<vector<type>> name(h, vector<type>(w));\IN(name)#define VVd(type, name, h, w)\vector<vector<type>> name(h, vector<type>(w));\IN2(name)int scan() { return getchar(); }void scan(int &a) { cin >> a; }void scan(long long &a) { cin >> a; }void scan(char &a) { cin >> a; }void scan(double &a) { cin >> a; }void scan(string &a) { cin >> a; }template <class T, class S> void scan(pair<T, S> &p) { scan(p.first), scan(p.second); }template <class T> void scan(vector<T> &);template <class T> void scan(vector<T> &a) {for(auto &i : a) scan(i);}template <class T> void scan(T &a) { cin >> a; }void IN() {}void IN2() {}template <class Head, class... Tail> void IN(Head &head, Tail &...tail) {scan(head);IN(tail...);}template <class Head, class... Tail> void IN2(Head &head, Tail &...tail) {scan(head);--head;IN2(tail...);}template <int p = -1> void pat() {}template <int p = -1, class Head, class... Tail> void pat(Head &h, Tail &...tail) {h += p;pat<p>(tail...);}template <typename T, typename S> T ceil(T x, S y) {assert(y);return (y < 0 ? ceil(-x, -y) : (x > 0 ? (x + y - 1) / y : x / y));}template <typename T, typename S> T floor(T x, S y) {assert(y);return (y < 0 ? floor(-x, -y) : (x > 0 ? x / y : x / y - (x % y == 0 ? 0 : 1)));}template <typename T, typename S, typename U> U bigmul(const T &x, const S &y, const U &lim) { // clamp(x * y, -lim, lim)if(x < 0 and y < 0) return bigmul(-x, -y, lim);if(x < 0) return -bigmul(-x, y, lim);if(y < 0) return -bigmul(x, -y, lim);return y == 0 or x <= lim / y ? x * y : lim;}template <class T> T POW(T x, int n) {T res = 1;for(; n; n >>= 1, x *= x)if(n & 1) res *= x;return res;}template <class T, class S> T POW(T x, S n, const ll &mod) {T res = 1;x %= mod;for(; n; n >>= 1, x = x * x % mod)if(n & 1) res = res * x % mod;return res;}vector<pll> factor(ll x) {vector<pll> ans;for(ll 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;}template <class T> vector<T> divisor(T x) {vector<T> ans;for(T i = 1; i * i <= x; i++)if(x % i == 0) {ans.pb(i);if(i * i != x) ans.pb(x / i);}return ans;}template <typename T> void zip(vector<T> &x) {vector<T> y = x;UNIQUE(y);for(int i = 0; i < x.size(); ++i) { x[i] = lb(y, x[i]); }}template <class S> void fold_in(vector<S> &v) {}template <typename Head, typename... Tail, class S> void fold_in(vector<S> &v, Head &&a, Tail &&...tail) {for(auto e : a) v.emplace_back(e);fold_in(v, tail...);}template <class S> void renumber(vector<S> &v) {}template <typename Head, typename... Tail, class S> void renumber(vector<S> &v, Head &&a, Tail &&...tail) {for(auto &&e : a) e = lb(v, e);renumber(v, tail...);}template <class S, class... Args> vector<S> zip(vector<S> &head, Args &&...args) {vector<S> v;fold_in(v, head, args...);sort(all(v)), v.erase(unique(all(v)), v.end());renumber(v, head, args...);return v;}template <typename S> void rearrange(const vector<S> &id) {}template <typename S, typename T> void rearrange_exec(const vector<S> &id, vector<T> &v) {vector<T> w(v.size());rep(i, si(id)) w[i] = v[id[i]];v.swap(w);}// 並び替える順番, 並び替える vector 達template <typename S, typename Head, typename... Tail> void rearrange(const vector<S> &id, Head &a, Tail &...tail) {rearrange_exec(id, a);rearrange(id, tail...);}template <typename T> vector<T> RUI(const vector<T> &v) {vector<T> res(v.size() + 1);for(int i = 0; i < v.size(); i++) res[i + 1] = res[i] + v[i];return res;}template <typename T> void zeta_supersetsum(vector<T> &f) {int n = f.size();for(int i = 1; i < n; i <<= 1) rep(b, n) if(!(i & b)) f[b] += f[b | i];}template <typename T> void zeta_subsetsum(vector<T> &f) {int n = f.size();for(int i = 1; i < n; i <<= 1) rep(b, n) if(!(i & b)) f[b | i] += f[b];}template <typename T> void mobius_subset(vector<T> &f) {int n = f.size();for(int i = 1; i < n; i <<= 1) rep(b, n) if(!(i & b)) f[b] -= f[b | i];}template <typename T> void mobius_superset(vector<T> &f) {int n = f.size();for(int i = 1; i < n; i <<= 1) rep(b, n) if(!(i & b)) f[b | i] -= f[b];}// 反時計周りに 90 度回転template <typename T> void rot(vector<vector<T>> &v) {if(empty(v)) return;int n = v.size(), m = v[0].size();vector<vector<T>> res(m, vector<T>(n));rep(i, n) rep(j, m) res[m - 1 - j][i] = v[i][j];v.swap(res);}vector<int> counter(const vector<int> &v, int max_num = -1) {if(max_num == -1) max_num = MAX(v);vector<int> res(max_num + 1);fore(e, v) res[e]++;return res;}// x in [l, r)template <class T, class S> bool inc(const T &x, const S &l, const S &r) { return l <= x and x < r; }template <class T, class S> bool inc(const T &x, const pair<S, S> &p) { return p.first <= x and x < p.second; }// 便利関数constexpr ll ten(int n) { return n == 0 ? 1 : ten(n - 1) * 10; }constexpr ll tri(ll n) { return n * (n + 1) / 2; }// l + ... + rconstexpr ll tri(ll l, ll r) { return (l + r) * (r - l + 1) / 2; }ll max(int x, ll y) { return max((ll)x, y); }ll max(ll x, int y) { return max(x, (ll)y); }int min(int x, ll y) { return min((ll)x, y); }int min(ll x, int y) { return min(x, (ll)y); }// bit 演算系#define bit(i) (1LL << i) // (1 << i)#define test(b, i) (b >> i & 1) // b の i bit 目が立っているかll pow2(int i) { return 1LL << i; }int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }int topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }int lowbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }int lowbit(ll a) { return a == 0 ? 64 : __builtin_ctzll(a); }// int allbit(int n) { return (1 << n) - 1; }constexpr ll mask(int n) { return (1LL << n) - 1; }// int popcount(signed t) { return __builtin_popcount(t); }// int popcount(ll t) { return __builtin_popcountll(t); }int popcount(uint64_t t) { return __builtin_popcountll(t); }static inline uint64_t popcount64(uint64_t x) {uint64_t m1 = 0x5555555555555555ll;uint64_t m2 = 0x3333333333333333ll;uint64_t m4 = 0x0F0F0F0F0F0F0F0Fll;uint64_t h01 = 0x0101010101010101ll;x -= (x >> 1) & m1;x = (x & m2) + ((x >> 2) & m2);x = (x + (x >> 4)) & m4;return (x * h01) >> 56;}bool ispow2(int i) { return i && (i & -i) == i; }ll rnd(ll l, ll r) { //[l, r)#ifdef noimistatic mt19937_64 gen;#elsestatic mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());#endifreturn uniform_int_distribution<ll>(l, r - 1)(gen);}ll rnd(ll n) { return rnd(0, n); }template <class t> void random_shuffle(vc<t> &a) { rep(i, si(a)) swap(a[i], a[rnd(0, i + 1)]); }int in() {int x;cin >> x;return x;}ll lin() {unsigned long long x;cin >> x;return x;}template <class T, class S> pair<T, S> operator-(const pair<T, S> &x) { return pair<T, S>(-x.first, -x.second); }template <class T, class S> pair<T, S> operator-(const pair<T, S> &x, const pair<T, S> &y) { return pair<T, S>(x.fi - y.fi, x.se - y.se); }template <class T, class S> pair<T, S> operator+(const pair<T, S> &x, const pair<T, S> &y) { return pair<T, S>(x.fi + y.fi, x.se + y.se); }template <class T> pair<T, T> operator&(const pair<T, T> &l, const pair<T, T> &r) { return pair<T, T>(max(l.fi, r.fi), min(l.se, r.se)); }template <class T, class S> pair<T, S> operator+=(pair<T, S> &l, const pair<T, S> &r) { return l = l + r; }template <class T, class S> pair<T, S> operator-=(pair<T, S> &l, const pair<T, S> &r) { return l = l - r; }template <class T> bool intersect(const pair<T, T> &l, const pair<T, T> &r) { return (l.se < r.se ? r.fi < l.se : l.fi < r.se); }template <class T> vector<T> &operator++(vector<T> &v) {fore(e, v) e++;return v;}template <class T> vector<T> operator++(vector<T> &v, int) {auto res = v;fore(e, v) e++;return res;}template <class T> vector<T> &operator--(vector<T> &v) {fore(e, v) e--;return v;}template <class T> vector<T> operator--(vector<T> &v, int) {auto res = v;fore(e, v) e--;return res;}template <class T> void connect(vector<T> &l, const vector<T> &r) { fore(e, r) l.eb(e); }template <class T> vector<T> operator+(const vector<T> &l, const vector<T> &r) {vector<T> res(max(si(l), si(r)));rep(i, si(l)) res[i] += l[i];rep(i, si(r)) res[i] += r[i];return res;}template <class T> vector<T> operator-(const vector<T> &l, const vector<T> &r) {vector<T> res(max(si(l), si(r)));rep(i, si(l)) res[i] += l[i];rep(i, si(r)) res[i] -= r[i];return res;}template <class T> vector<T> &operator+=(const vector<T> &l, const vector<T> &r) {if(si(l) < si(r)) l.resize(si(r));rep(i, si(r)) l[i] += r[i];return l;}template <class T> vector<T> &operator-=(const vector<T> &l, const vector<T> &r) {if(si(l) < si(r)) l.resize(si(r));rep(i, si(r)) l[i] -= r[i];return l;}template <class T> vector<T> &operator+=(vector<T> &v, const T &x) {fore(e, v) e += x;return v;}template <class T> vector<T> &operator-=(vector<T> &v, const T &x) {fore(e, v) e -= x;return v;}template <typename T> struct edge {int from, to;T cost;int id;edge(int to, T cost) : from(-1), to(to), cost(cost) {}edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}edge(int from, int to, T cost, int id) : from(from), to(to), cost(cost), id(id) {}constexpr bool operator<(const edge<T> &rhs) const noexcept { return cost < rhs.cost; }edge &operator=(const int &x) {to = x;return *this;}operator int() const { return to; }friend ostream operator<<(ostream &os, const edge &e) { return os << e.to; }};template <typename T> using Edges = vector<edge<T>>;template <typename T = int> Edges<T> read_edges(int m, bool weighted = false) {Edges<T> res;res.reserve(m);for(int i = 0; i < m; i++) {int u, v, c = 0;scan(u), scan(v), u--, v--;if(weighted) scan(c);res.eb(u, v, c, i);}return res;}using Tree = vector<vector<int>>;using Graph = vector<vector<int>>;template <class T> using Wgraph = vector<vector<edge<T>>>;Graph getG(int n, int m = -1, bool directed = false, int margin = 1) {Tree res(n);if(m == -1) m = n - 1;while(m--) {int a, b;cin >> a >> b;a -= margin, b -= margin;res[a].emplace_back(b);if(!directed) res[b].emplace_back(a);}return res;}Graph getTreeFromPar(int n, int margin = 1) {Graph res(n);for(int i = 1; i < n; i++) {int a;cin >> a;res[a - margin].emplace_back(i);}return res;}template <class T> Wgraph<T> getWg(int n, int m = -1, bool directed = false, int margin = 1) {Wgraph<T> res(n);if(m == -1) m = n - 1;while(m--) {int a, b;T c;scan(a), scan(b), scan(c);a -= margin, b -= margin;res[a].emplace_back(b, c);if(!directed) res[b].emplace_back(a, c);}return res;}void add(Graph &G, int x, int y) { G[x].eb(y), G[y].eb(x); }template <class S, class T> void add(Wgraph<S> &G, int x, int y, T c) { G[x].eb(y, c), G[y].eb(x, c); }#define TEST\INT(testcases);\while(testcases--)i128 abs(const i128 &x) { return x > 0 ? x : -x; }istream &operator>>(istream &is, i128 &v) {string s;is >> s;v = 0;for(int i = 0; i < (int)s.size(); i++) {if(isdigit(s[i])) { v = v * 10 + s[i] - '0'; }}if(s[0] == '-') { v *= -1; }return is;}ostream &operator<<(ostream &os, const i128 &v) {if(v == 0) { return (os << "0"); }i128 num = v;if(v < 0) {os << '-';num = -num;}string s;for(; num > 0; num /= 10) { s.push_back((char)(num % 10) + '0'); }reverse(s.begin(), s.end());return (os << s);}namespace aux {template <typename T, unsigned N, unsigned L> struct tp {static void output(std::ostream &os, const T &v) {os << std::get<N>(v) << (&os == &cerr ? ", " : " ");tp<T, N + 1, L>::output(os, v);}};template <typename T, unsigned N> struct tp<T, N, N> {static void output(std::ostream &os, const T &v) { os << std::get<N>(v); }};} // namespace auxtemplate <typename... Ts> std::ostream &operator<<(std::ostream &os, const std::tuple<Ts...> &t) {if(&os == &cerr) { os << '('; }aux::tp<std::tuple<Ts...>, 0, sizeof...(Ts) - 1>::output(os, t);if(&os == &cerr) { os << ')'; }return os;}template <typename T, typename S, typename U> std::ostream &operator<<(std::ostream &os, const priority_queue<T, S, U> &_pq) {auto pq = _pq;vector<T> res;while(!empty(pq)) res.emplace_back(pq.top()), pq.pop();return os << res;}template <class T, class S> ostream &operator<<(ostream &os, const pair<T, S> &p) {if(&os == &cerr) { return os << "(" << p.first << ", " << p.second << ")"; }return os << p.first << " " << p.second;}template <class Ch, class Tr, class Container> std::basic_ostream<Ch, Tr> &operator<<(std::basic_ostream<Ch, Tr> &os, const Container &x) {bool f = true;if(&os == &cerr) os << "[";for(auto &y : x) {if(&os == &cerr)os << (f ? "" : ", ") << y;elseos << (f ? "" : " ") << y;f = false;}if(&os == &cerr) os << "]";return os;}#define dump(...) static_cast<void>(0)#define dbg(...) static_cast<void>(0)void OUT() { cout << endl; }template <class Head, class... Tail> void OUT(const Head &head, const Tail &...tail) {cout << head;if(sizeof...(tail)) cout << ' ';OUT(tail...);}template <typename T> static constexpr T inf = numeric_limits<T>::max() / 2;template <class T, class S> constexpr pair<T, S> inf<pair<T, S>> = {inf<T>, inf<S>};template <class T> void OUT2(const T &t, T INF = inf<T>, T res = -1) { OUT(t != INF ? t : res); }template <class T> void OUT2(vector<T> &v, T INF = inf<T>, T res = -1) {fore(e, v) if(e == INF) e = res;OUT(v);fore(e, v) if(e == res) e = INF;}template <class F> struct REC {F f;REC(F &&f_) : f(forward<F>(f_)) {}template <class... Args> auto operator()(Args &&...args) const { return f(*this, forward<Args>(args)...); }};template <class S> vector<pair<S, int>> runLength(const vector<S> &v) {vector<pair<S, int>> res;for(auto &e : v) {if(res.empty() or res.back().fi != e)res.eb(e, 1);elseres.back().se++;}return res;}vector<pair<char, int>> runLength(const string &v) {vector<pair<char, int>> res;for(auto &e : v) {if(res.empty() or res.back().fi != e)res.eb(e, 1);elseres.back().se++;}return res;}struct string_converter {char start = 0;char type(const char &c) const { return (islower(c) ? 'a' : isupper(c) ? 'A' : isdigit(c) ? '0' : 0); }int convert(const char &c) {if(!start) start = type(c);return c - start;}int convert(const char &c, const string &chars) { return chars.find(c); }template <typename T> auto convert(const T &v) {vector<decltype(convert(v[0]))> ret;ret.reserve(size(v));for(auto &&e : v) ret.emplace_back(convert(e));return ret;}template <typename T> auto convert(const T &v, const string &chars) {vector<decltype(convert(v[0], chars))> ret;ret.reserve(size(v));for(auto &&e : v) ret.emplace_back(convert(e, chars));return ret;}int operator()(const char &v, char s = 0) {start = s;return convert(v);}int operator()(const char &v, const string &chars) { return convert(v, chars); }template <typename T> auto operator()(const T &v, char s = 0) {start = s;return convert(v);}template <typename T> auto operator()(const T &v, const string &chars) { return convert(v, chars); }} toint;template <class T, class F> T bin_search(T ok, T ng, const F &f) {while(abs(ok - ng) > 1) {T mid = ok + ng >> 1;(f(mid) ? ok : ng) = mid;}return ok;}template <class T, class F> T bin_search_double(T ok, T ng, const F &f, int iter = 80) {while(iter--) {T mid = (ok + ng) / 2;(f(mid) ? ok : ng) = mid;}return ok;}struct Setup_io {Setup_io() {ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);cout << fixed << setprecision(11);}} setup_io;#endif#pragma endregionnamespace modular {constexpr int MOD = 998244353;const int MAXN = 11000000;template <int Modulus> class modint;using mint = modint<MOD>;using vmint = vector<mint>;vector<mint> Inv;mint inv(int x);template <int Modulus> class modint {public:static constexpr int mod() { return Modulus; }int a;constexpr modint(const ll x = 0) noexcept : a(((x % Modulus) + Modulus) % Modulus) {}constexpr int &val() noexcept { return a; }constexpr const int &val() const noexcept { return a; }constexpr modint operator-() const noexcept { return modint() - *this; }constexpr modint operator+() const noexcept { return *this; }constexpr modint &operator++() noexcept {if(++a == MOD) a = 0;return *this;}constexpr modint &operator--() noexcept {if(!a) a = MOD;a--;return *this;}constexpr modint operator++(int) {modint res = *this;++*this;return res;}constexpr modint operator--(int) {mint res = *this;--*this;return res;}constexpr modint &operator+=(const modint rhs) noexcept {a += rhs.a;if(a >= Modulus) { a -= Modulus; }return *this;}constexpr modint &operator-=(const modint rhs) noexcept {if(a < rhs.a) { a += Modulus; }a -= rhs.a;return *this;}constexpr modint &operator*=(const modint rhs) noexcept {a = (long long)a * rhs.a % Modulus;return *this;}constexpr modint &operator/=(const modint rhs) noexcept {a = (long long)a * (modular::inv(rhs.a)).a % Modulus;return *this;}constexpr modint pow(long long n) const noexcept {if(n < 0) {n %= Modulus - 1;n = (Modulus - 1) + n;}modint x = *this, r = 1;while(n) {if(n & 1) r *= x;x *= x;n >>= 1;}return r;}constexpr modint inv() const noexcept { return pow(Modulus - 2); }constexpr friend modint operator+(const modint &lhs, const modint &rhs) { return modint(lhs) += modint(rhs); }constexpr friend modint operator-(const modint &lhs, const modint &rhs) { return modint(lhs) -= modint(rhs); }constexpr friend modint operator*(const modint &lhs, const modint &rhs) { return modint(lhs) *= modint(rhs); }constexpr friend modint operator/(const modint &lhs, const modint &rhs) { return modint(lhs) /= modint(rhs); }constexpr friend bool operator==(const modint &lhs, const modint &rhs) { return lhs.a == rhs.a; }constexpr friend bool operator!=(const modint &lhs, const modint &rhs) { return lhs.a != rhs.a; }// constexpr friend modint operator^=(const modint &lhs, const modint &rhs) { return modint(lhs) ^= modint(rhs); }};vmint Fact{1, 1}, Ifact{1, 1};mint inv(int n) {if(n > MAXN) return (mint(n)).pow(MOD - 2);if(Inv.empty()) Inv.emplace_back(0), Inv.emplace_back(1);if(Inv.size() > n)return Inv[n];else {for(int i = Inv.size(); i <= n; ++i) {auto [y, x] = div(int(MOD), i);Inv.emplace_back(Inv[x] * (-y));}return Inv[n];}}mint fact(int n) {if(Fact.size() > n)return Fact[n];elsefor(int i = Fact.size(); i <= n; ++i) Fact.emplace_back(Fact[i - 1] * i);return Fact[n];}mint ifact(int n) {if(Ifact.size() > n)return Ifact[n];elsefor(int i = Ifact.size(); i <= n; ++i) Ifact.emplace_back(Ifact[i - 1] * inv(i));return Ifact[n];}mint modpow(ll a, ll n) { return mint(a).pow(n); }mint inv(mint a) { return inv(a.a); }mint ifact(mint a) { return ifact(a.a); }mint fact(mint a) { return fact(a.a); }mint modpow(mint a, ll n) { return modpow(a.a, n); }mint C(int a, int b) {if(a < 0 || b < 0) return 0;if(a < b) return 0;if(a > MAXN) {mint res = 1;rep(i, b) res *= a - i, res /= i + 1;return res;}return fact(a) * ifact(b) * ifact(a - b);}mint P(int a, int b) {if(a < 0 || b < 0) return 0;if(a < b) return 0;if(a > MAXN) {mint res = 1;rep(i, b) res *= a - i;return res;}return fact(a) * ifact(a - b);}ostream &operator<<(ostream &os, mint a) {os << a.a;return os;}istream &operator>>(istream &is, mint &a) {ll x;is >> x;a = x;return is;}ostream &operator<<(ostream &os, const vmint &a) {if(!a.empty()) {os << a[0];for(int i = 1; i < si(a); i++) os << " " << a[i];}return os;}#ifdef _MSC_VER#include <intrin.h>#endifnamespace convolution {namespace internal {int ceil_pow2(int n) {int x = 0;while((1U << x) < (unsigned int)(n)) x++;return x;}int bsf(unsigned int n) {#ifdef _MSC_VERunsigned long index;_BitScanForward(&index, n);return index;#elsereturn __builtin_ctz(n);#endif}constexpr long long safe_mod(long long x, long long m) {x %= m;if(x < 0) x += m;return x;}struct barrett {unsigned int _m;unsigned long long im;barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}unsigned int umod() const { return _m; }unsigned int mul(unsigned int a, unsigned int b) const {unsigned long long z = a;z *= b;#ifdef _MSC_VERunsigned long long x;_umul128(z, im, &x);#elseunsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64);#endifunsigned int v = (unsigned int)(z - x * _m);if(_m <= v) v += _m;return v;}};constexpr long long pow_mod_constexpr(long long x, long long n, int m) {if(m == 1) return 0;unsigned int _m = (unsigned int)(m);unsigned long long r = 1;unsigned long long 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;long long d = n - 1;while(d % 2 == 0) d /= 2;for(long long a : {2, 7, 61}) {long long t = d;long long 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 = 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; // |m1 * u| <= |m1| * s <= bauto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}if(m0 < 0) m0 += b / s;return {s, m0};}// Compile time primitive root// @param m must be prime// @return primitive root (and minimum in now)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; (long long)(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 = primitive_root_constexpr(m);void butterfly(std::vector<mint> &a) {static constexpr int g = internal::primitive_root<mint::mod()>;int n = int(a.size());int h = internal::ceil_pow2(n);static bool first = true;static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]if(first) {first = false;mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1int cnt2 = bsf(mint::mod() - 1);mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();for(int i = cnt2; i >= 2; i--) {// e^(2^i) == 1es[i - 2] = e;ies[i - 2] = ie;e *= e;ie *= ie;}mint now = 1;for(int i = 0; i < cnt2 - 2; i++) {sum_e[i] = es[i] * now;now *= ies[i];}}for(int ph = 1; ph <= h; ph++) {int w = 1 << (ph - 1), p = 1 << (h - ph);mint now = 1;for(int s = 0; s < w; s++) {int offset = s << (h - ph + 1);for(int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p] * now;a[i + offset] = l + r;a[i + offset + p] = l - r;}now *= sum_e[bsf(~(unsigned int)(s))];}}}void butterfly_inv(std::vector<mint> &a) {static constexpr int g = internal::primitive_root<mint::mod()>;int n = int(a.size());int h = internal::ceil_pow2(n);static bool first = true;static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]if(first) {first = false;mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1int cnt2 = bsf(mint::mod() - 1);mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();for(int i = cnt2; i >= 2; i--) {// e^(2^i) == 1es[i - 2] = e;ies[i - 2] = ie;e *= e;ie *= ie;}mint now = 1;for(int i = 0; i < cnt2 - 2; i++) {sum_ie[i] = ies[i] * now;now *= es[i];}}for(int ph = h; ph >= 1; ph--) {int w = 1 << (ph - 1), p = 1 << (h - ph);mint inow = 1;for(int s = 0; s < w; s++) {int offset = s << (h - ph + 1);for(int i = 0; i < p; i++) {auto l = a[i + offset];auto r = a[i + offset + p];a[i + offset] = l + r;a[i + offset + p] = (unsigned long long)(mint::mod() + l.val() - r.val()) * inow.val();}inow *= sum_ie[bsf(~(unsigned int)(s))];}}mint z = mint(n).inv();for(int i = 0; i < n; i++) a[i] *= z;}} // namespace internalstd::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {int n = int(a.size()), m = int(b.size());if(!n || !m) return {};if(std::min(n, m) <= 60) {if(n < m) {std::swap(n, m);std::swap(a, b);}std::vector<mint> ans(n + m - 1);for(int i = 0; i < n; i++) {for(int j = 0; j < m; j++) { ans[i + j] += a[i] * b[j]; }}return ans;}int z = 1 << internal::ceil_pow2(n + m - 1);a.resize(z);internal::butterfly(a);b.resize(z);internal::butterfly(b);for(int i = 0; i < z; i++) { a[i] *= b[i]; }internal::butterfly_inv(a);a.resize(n + m - 1);// mint iz = mint(z).inv();// for(int i = 0; i < n + m - 1; i++) a[i] *= iz;return a;}} // namespace convolutionusing Poly = vmint;Poly low(const Poly &f, int s) { return Poly(f.begin(), f.begin() + min<int>(max(s, 1), f.size())); }Poly operator-(Poly f) {for(auto &&e : f) e = -e;return f;}Poly &operator+=(Poly &l, const Poly &r) {l.resize(max(l.size(), r.size()));rep(i, r.size()) l[i] += r[i];return l;}Poly operator+(Poly l, const Poly &r) { return l += r; }Poly &operator-=(Poly &l, const Poly &r) {l.resize(max(l.size(), r.size()));rep(i, r.size()) l[i] -= r[i];return l;}Poly operator-(Poly l, const Poly &r) { return l -= r; }Poly &operator<<=(Poly &f, size_t n) { return f.insert(f.begin(), n, 0), f; }Poly operator<<(Poly f, size_t n) { return f <<= n; }Poly &operator>>=(Poly &f, size_t n) { return f.erase(f.begin(), f.begin() + min(f.size(), n)), f; }Poly operator>>(Poly f, size_t n) { return f >>= n; }Poly operator*(const Poly &l, const Poly &r) { return convolution::convolution(l, r); }Poly &operator*=(Poly &l, const Poly &r) { return l = l * r; }Poly &operator*=(Poly &l, const mint &x) {for(auto &e : l) e *= x;return l;}Poly operator*(const Poly &l, const mint &x) {auto res = l;return res *= x;}Poly inv(const Poly &f, int s = -1) {if(s == -1) s = f.size();Poly r(s);r[0] = mint(1) / f[0];for(int n = 1; n < s; n *= 2) {auto F = low(f, 2 * n);F.resize(2 * n);convolution::internal::butterfly(F);auto g = low(r, 2 * n);g.resize(2 * n);convolution::internal::butterfly(g);rep(i, 2 * n) F[i] *= g[i];convolution::internal::butterfly_inv(F);rep(i, n) F[i] = 0;convolution::internal::butterfly(F);rep(i, 2 * n) F[i] *= g[i];convolution::internal::butterfly_inv(F);rep(i, n, min(2 * n, s)) r[i] -= F[i];}return r;}Poly integ(const Poly &f) {Poly res(f.size() + 1);for(int i = 1; i < (int)res.size(); ++i) res[i] = f[i - 1] / i;return res;}Poly deriv(const Poly &f) {if(f.size() == 0) return Poly();Poly res(f.size() - 1);rep(i, res.size()) res[i] = f[i + 1] * (i + 1);return res;}Poly log(const Poly &f) {Poly g = integ(inv(f) * deriv(f));return Poly{g.begin(), g.begin() + f.size()};}Poly exp(const Poly &f) {Poly g{1};while(g.size() < f.size()) {Poly x(f.begin(), f.begin() + min(f.size(), g.size() * 2));x[0] += 1;g.resize(2 * g.size());x -= log(g);x *= {g.begin(), g.begin() + g.size() / 2};rep(i, g.size() / 2, min<int>(x.size(), g.size())) g[i] = x[i];}return {g.begin(), g.begin() + f.size()};}Poly pow(const Poly &f, ll k, int need = -1) {const int n = (int)f.size();if(need == -1) need = n;int z = 0;rep(i, n) {if(f[i].a) break;z++;}if(z * k >= need) return Poly(n);mint rev = f[z].inv();Poly res = exp(log((f >> z) * rev) * k) * f[z].pow(k);res.resize(need - z * k);return res << z * k;}struct Prd {deque<Poly> deq;Prd() = default;void emplace(const Poly &f) { deq.emplace_back(f); }Poly calc() {if(deq.empty()) return {1};sort(all(deq), [&](const Poly &f, const Poly &g) { return si(f) < si(g); });while(deq.size() > 1) {deq.emplace_back(deq[0] * deq[1]);for(int i = 0; i < 2; ++i) deq.pop_front();}return deq.front();}};Poly prd(vector<Poly> &v) {Prd p;for(auto &e : v) p.emplace(e);return p.calc();}vmint power_table(mint x, int len) {vmint res(len + 1);res[0] = 1;rep(i, len) res[i + 1] = res[i] * x;return res;}// calc f(x + a)Poly TaylorShift(Poly f, mint a) {int n = f.size();rep(i, n) f[i] *= fact(i);reverse(all(f));Poly g(n, 1);rep(i, 1, n) g[i] = g[i - 1] * a * inv(i);f = (f * g);f.resize(n);reverse(begin(f), end(f));rep(i, n) f[i] *= ifact(i);return f;}} // namespace modularusing namespace modular;// from ACLnamespace lazysegtree_impl {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`constexpr int bsf_constexpr(unsigned int n) {int x = 0;while(!(n & (1 << x))) 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_VERunsigned long index;_BitScanForward(&index, n);return index;#elsereturn __builtin_ctz(n);#endif}} // namespace internal} // namespace lazysegtree_implnamespace lazysegtree_impl {template <class S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S), F (*composition)(F, F), F (*id)()> struct lazy_segtree {public:lazy_segtree() : lazy_segtree(0) {}explicit lazy_segtree(int n) : lazy_segtree(std::vector<S>(n, e())) {}explicit lazy_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());lz = std::vector<F>(size, id());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;for(int i = log; i >= 1; i--) push(p >> i);d[p] = x;for(int i = 1; i <= log; i++) update(p >> i);}S get(int p) {assert(0 <= p && p < _n);p += size;for(int i = log; i >= 1; i--) push(p >> i);return d[p];}S prod(int l, int r) {#ifdef ONLINE_JUDGEif(l < 0) l = 0;if(r > _n) r = _n;if(l > r) return e();#endifassert(0 <= l && l <= r && r <= _n);if(l == r) return e();l += size;r += size;for(int i = log; i >= 1; i--) {if(((l >> i) << i) != l) push(l >> i);if(((r >> i) << i) != r) push((r - 1) >> i);}S sml = e(), smr = e();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]; }void apply(int p, F f) {assert(0 <= p && p < _n);p += size;for(int i = log; i >= 1; i--) push(p >> i);d[p] = mapping(f, d[p]);for(int i = 1; i <= log; i++) update(p >> i);}void apply(int l, int r, F f) {#ifdef ONLINE_JUDGEif(l < 0) l = 0;if(r > _n) r = _n;if(l > r) return;#endifassert(0 <= l && l <= r && r <= _n);if(l == r) return;l += size;r += size;for(int i = log; i >= 1; i--) {if(((l >> i) << i) != l) push(l >> i);if(((r >> i) << i) != r) push((r - 1) >> i);}{int l2 = l, r2 = r;while(l < r) {if(l & 1) all_apply(l++, f);if(r & 1) all_apply(--r, f);l >>= 1;r >>= 1;}l = l2;r = r2;}for(int i = 1; i <= log; i++) {if(((l >> i) << i) != l) update(l >> i);if(((r >> i) << i) != r) update((r - 1) >> i);}}template <bool (*g)(S)> int max_right(int l) {return max_right(l, [](S x) { return g(x); });}template <class G> int max_right(int l, G g) {#ifdef ONLINE_JUDGEif(l < 0) l = 0;if(l > _n) l = _n;#endifassert(0 <= l && l <= _n);assert(g(e()));if(l == _n) return _n;l += size;for(int i = log; i >= 1; i--) push(l >> i);S sm = e();do {while(l % 2 == 0) l >>= 1;if(!g(op(sm, d[l]))) {while(l < size) {push(l);l = (2 * l);if(g(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 (*g)(S)> int min_left(int r) {return min_left(r, [](S x) { return g(x); });}template <class G> int min_left(int r, G g) {#ifdef ONLINE_JUDGEif(r < 0) r = 0;if(r > _n) r = _n;#endifassert(0 <= r && r <= _n);assert(g(e()));if(r == 0) return 0;r += size;for(int i = log; i >= 1; i--) push((r - 1) >> i);S sm = e();do {r--;while(r > 1 && (r % 2)) r >>= 1;if(!g(op(d[r], sm))) {while(r < size) {push(r);r = (2 * r + 1);if(g(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;}S operator[](int k) { return get(k); }friend std::ostream &operator<<(std::ostream &os, lazy_segtree &ls) {os << "{";for(int i = 0; i < ls._n; i++) os << ls.get(i) << (i == ls._n - 1 ? "" : ", ");return os << "}";}int len() { return _n; }private:int _n, size, log;std::vector<S> d;std::vector<F> lz;void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); }void all_apply(int k, F f) {d[k] = mapping(f, d[k]);if(k < size) lz[k] = composition(f, lz[k]);}void push(int k) {all_apply(2 * k, lz[k]);all_apply(2 * k + 1, lz[k]);lz[k] = id();}};template <class T> constexpr T inf = std::numeric_limits<T>::max() / 2;template <class T, class U> constexpr std::pair<T, U> inf<std::pair<T, U>> = {inf<T>, inf<U>};template <typename T> T min_func(T x, T y) { return min(x, y); }template <typename T> T max_func(T x, T y) { return max(x, y); }template <typename T> T plus_func(T x, T y) { return x + y; }template <typename T, int ID> T set_func(T x, T y) { return (y == ID ? x : y); }template <typename T> T min_e() { return inf<T>; }template <typename T> T max_e() { return -inf<T>; }template <typename T> T plus_e() { return T(); }// range add get range mintemplate <typename T> using RARm = lazy_segtree<T, min_func<T>, min_e<T>, T, plus_func<T>, plus_func<T>, plus_e<T>>;// range add get range maxtemplate <typename T> using RARM = lazy_segtree<T, max_func<T>, max_e<T>, T, plus_func<T>, plus_func<T>, plus_e<T>>;// range add get range sum// first が size, second が valuetemplate <typename T> pair<int, T> RARS_op(pair<int, T> x, pair<int, T> y) { return {x.first + y.first, x.second + y.second}; }template <typename T> pair<int, T> RARS_e() { return {0, 0}; }template <typename T> pair<int, T> RARS_map(T f, pair<int, T> x) { return {x.first, x.second + f * x.first}; }template <typename T> using _RARS = lazy_segtree<pair<int, T>, RARS_op<T>, RARS_e<T>, T, RARS_map<T>, plus_func<T>, plus_e<T>>;template <typename T> struct RARS : _RARS<T> {private:vector<pair<int, T>> to_p(const vector<T> &v) {vector<pair<int, T>> res(v.size());for(int i = 0; i < v.size(); i++) res[i] = pair(1, v[i]);return res;}public:RARS(int n) : _RARS<T>(vector(n, pair(1, T()))) {}RARS(const vector<T> &v) : _RARS<T>(to_p(v)) {}T get(int k) { return _RARS<T>::get(k).se; }T prod(int l, int r) { return _RARS<T>::prod(l, r).se; }T operator[](int k) { return get(k); }friend std::ostream &operator<<(std::ostream &os, RARS &ls) {os << "{";for(int i = 0; i < ls.len(); i++) os << ls.get(i) << (i == ls.len() ? "" : ", ");return os << "}";}};// 区間の挿入、削除、union のサイズ取得pair<int, int> segunion_merge(pair<int, int> x, pair<int, int> y) { return (x.se == y.se ? pair<int, int>{x.fi + y.fi, x.se} : x.se < y.se ? x : y);}pair<int, int> segunion_e() { return {}; }pair<int, int> segunion_mapp(int x, pair<int, int> p) { return {p.fi, p.se + x}; }using SegmentUnion = lazy_segtree<pair<int, int>, segunion_merge, segunion_e, int, segunion_mapp, plus_func<int>, plus_e<int>>;} // namespace lazysegtree_implusing lazysegtree_impl::lazy_segtree;using lazysegtree_impl::RARM;using lazysegtree_impl::RARm;using lazysegtree_impl::RARS;using lazysegtree_impl::SegmentUnion;template <typename T> struct BinaryIndexedTree {vector<T> data;BinaryIndexedTree(int sz) { data.assign(++sz, 0); }T sum(int k) {T ret = 0;for(++k; k > 0; k -= k & -k) ret += data[k];return (ret);}void add(int k, T x) {for(++k; k < data.size(); k += k & -k) data[k] += x;}};#define BIT BinaryIndexedTreetemplate <typename T> long long inversion(vector<T> a, bool is_zip = true) {if(!is_zip) {vector<T> id(a.size());for(int i = 0; i < a.size(); ++i) id[i] = a[i];sort(id.begin(), id.end());for(int i = 0; i < a.size(); ++i) a[i] = lower_bound(id.begin(), id.end(), a[i]) - id.begin();}BIT<int> bitt(a.size() + 1);long long res = (long long)a.size() * (a.size() - 1) / 2;for(int i = 0; i < a.size(); ++i) {res -= bitt.sum(a[i]);bitt.add(a[i], 1);}return res;}int main() {INT(n, m);VEC2(int, k, p, m);fore(e, p) e--;fore(e, k) e--;vi used(n);rep(i, m) used[k[i]] = p[i] + 1;vi ret(n);rep(i, m) ret[p[i]] = true;vi v;rep(i, n) if(!ret[i]) v.eb(i);RARS<ll> seg(si(v));int S = 0;fore(e, used) if(!e) S++;mint ans;// OUT(v);// OUT(used);rep(i, n) {if(used[i]) {int t = used[i] - 1;int x = lb(v, t);seg.apply(x, si(v), 1);}}rep(i, n) {if(used[i]) {int t = used[i] - 1;int x = lb(v, t);seg.apply(0, x, 1);seg.apply(x, si(v), -1);// OUT(x);// OUT(i);} else {// fore(e, v) {// int c = 0;// rep(j, m) {// if(p[j] < e and k[j] > i) c++;// if(p[j] > e and k[j] < i) c++;// }// ans += c * fact(S - 1);// }ans += fact(S - 1) * seg.all_prod().se;}}vpi w;rep(i, m) w.eb(p[i], k[i]);SORT(w);vi x;fore(a, b, w) x.eb(b);ans += fact(S) * inversion(x, false);OUT(ans + fact(S) * S * (S - 1) * inv(4));}