結果
問題 | No.2327 Inversion Sum |
ユーザー |
👑 |
提出日時 | 2023-05-28 15:18:39 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 138 ms / 2,000 ms |
コード長 | 42,904 bytes |
コンパイル時間 | 2,449 ms |
コンパイル使用メモリ | 226,344 KB |
最終ジャッジ日時 | 2025-02-13 12:56:31 |
ジャッジサーバーID (参考情報) |
judge5 / judge3 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 30 |
ソースコード
// line 1 "answer.cpp"#if !__INCLUDE_LEVEL__#include __FILE__int main() {ll n,m;input(n,m);using mint = modint998244353;vl pos(n, -1);vl a(n, -1);lseg_add_radd<ll> seg(n-m);rep(i, m) {ll pi, ki;input(pi,ki);--ki; --pi;a[ki] = pi;pos[pi] = ki;}vl ai, ai2;rep(i, n) {if(a[i]!= -1) ai.push_back(a[i]);}debug(ai);mint ans = inversion_number(ai);mint fact = 1;rep(i, 1, n-m+1) fact *= i;ans *= fact;fact = 1;rep(i, 1, n-m) fact *= i;Combination<mint> comb(100000);mint ti = 1;rep(i, 1, n-m-1) ti *= i;ti *= comb(n-m, 2);ti *= comb(n-m, 2);ans += ti;debug(pos);ll c = 0;rep(i, n) {if (a[i] != -1) {pos[a[i]] -= c;c++;}}debug(pos);rep(i, n) {if (pos[i] != -1) {seg.apply(0, pos[i], 1);}}debug(fact);debug(seg);debug(ans);rep(i, n-1, -1, -1) {if (pos[i] != -1) {seg.apply(0, pos[i], -1);} else {mint ti = mint(seg.all_prod().value);ti *= fact;ans += ti;}debug(seg);}rep(i, n-1, -1, -1) {if (pos[i] != -1) {seg.apply(pos[i], seg.n(), 1);} else {mint ti = mint(seg.all_prod().value);ti *= fact;ans += ti;}debug(seg);}print(ans);}#else// line 2 "/Users/seekworser/.cpp_lib/competitive_library/competitive/std/std.hpp"#include <bits/stdc++.h>#ifndef LOCAL_TEST#pragma GCC target ("avx")#pragma GCC optimize("O3")#pragma GCC optimize("unroll-loops")#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")#endif // LOCAL_TESTusing namespace std;// 型名の短縮using ll = long long;using pii = pair<int, int>; using pll = pair<ll, ll>;using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>;using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>;using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;using vs = vector<string>; using vvs = vector<vector<string>>; using vvvs = vector<vector<vector<string>>>;template<typename T> vector<vector<T>> vv(int h, int w, T val = T()) { return vector(h, vector<T>(w, val)); }template<typename T> vector<vector<vector<T>>> vvv(int h1, int h2, int h3, T val = T()) { return vector(h1, vector(h2, vector<T>(h3, val))); }template<typename T> vector<vector<vector<vector<T>>>> vvvv(int h1, int h2, int h3, int h4, T val = T()) { return vector(h1, vector(h2, vector(h3,vector<T>(h4, val)))); }template <class T> using priority_queue_min = priority_queue<T, vector<T>, greater<T>>;// 定数の定義constexpr double PI = 3.14159265358979323;constexpr int INF = 100100111; constexpr ll INFL = 3300300300300300491LL;float EPS = 1e-8; double EPSL = 1e-16;template<typename T> bool eq(const T x, const T y) { return x == y; }template<> bool eq<double>(const double x, const double y) { return abs(x - y) < EPSL; }template<> bool eq<float>(const float x, const float y) { return abs(x - y) < EPS; }template<typename T> bool neq(const T x, const T y) { return !(eq<T>(x, y)); }template<typename T> bool ge(const T x, const T y) { return (eq<T>(x, y) || (x > y)); }template<typename T> bool le(const T x, const T y) { return (eq<T>(x, y) || (x < y)); }template<typename T> bool gt(const T x, const T y) { return !(le<T>(x, y)); }template<typename T> bool lt(const T x, const T y) { return !(ge<T>(x, y)); }constexpr int MODINT998244353 = 998244353;constexpr int MODINT1000000007 = 1000000007;// 入出力高速化struct Nyan { Nyan() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } nyan;// 汎用マクロの定義#define all(a) (a).begin(), (a).end()#define sz(x) ((ll)(x).size())#define rep1(n) for(ll dummy_iter = 0LL; dummy_iter < n; ++dummy_iter) // 0 から n-1 まで昇順#define rep2(i, n) for(ll i = 0LL, i##_counter = 0LL; i##_counter < ll(n); ++(i##_counter), (i) = i##_counter) // 0 から n-1 まで昇順#define rep3(i, s, t) for(ll i = ll(s), i##_counter = ll(s); i##_counter < ll(t); ++(i##_counter), (i) = (i##_counter)) // s から t まで昇順#define rep4(i, s, t, step) for(ll i##_counter = step > 0 ? ll(s) : -ll(s), i##_end = step > 0 ? ll(t) : -ll(t), i##_step = abs(step), i = ll(s);i##_counter < i##_end; i##_counter += i##_step, i = step > 0 ? i##_counter : -i##_counter) // s から t まで stepずつ#define overload4(a, b, c, d, e, ...) e#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)#define repe(a, v) for(auto& a : (v)) // v の全要素(変更可能)#define smod(n, m) ((((n) % (m)) + (m)) % (m)) // 非負mod#define sdiv(n, m) (((n) - smod(n, m)) / (m)) // 非負div#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去int Yes(bool b=true) { cout << (b ? "Yes\n" : "No\n"); return 0; };int YES(bool b=true) { cout << (b ? "YES\n" : "NO\n"); return 0; };int No(bool b=true) {return Yes(!b);};int NO(bool b=true) {return YES(!b);};template<typename T, size_t N> T max(array<T, N>& a) { return *max_element(all(a)); };template<typename T, size_t N> T min(array<T, N>& a) { return *min_element(all(a)); };template<typename T> T max(vector<T>& a) { return *max_element(all(a)); };template<typename T> T min(vector<T>& a) { return *min_element(all(a)); };template<typename T> vector<T> vec_slice(const vector<T>& a, int l, int r) { vector<T> rev; rep(i, l, r) rev.push_back(a[i]); return rev; };template<typename T> T sum(vector<T>& a, T zero = T(0)) { T rev = zero; rep(i, sz(a)) rev += a[i]; return rev; };template<typename T> bool in_range(const T& val, const T& s, const T& t) { return s <= val && val < t; };template <class T> inline vector<T>& operator--(vector<T>& v) { repe(x, v) --x; return v; }template <class T> inline vector<T>& operator++(vector<T>& v) { repe(x, v) ++x; return v; }// modでのpowll powm(ll a, ll n, ll mod=INFL) {ll res = 1;while (n > 0) {if (n & 1) res = (res * a) % mod;if (n > 1) a = (a * a) % mod;n >>= 1;}return res;}// 整数Sqrtll sqrtll(ll x) {assert(x >= 0);ll rev = sqrt(x);while(rev * rev > x) --rev;while((rev+1) * (rev+1)<=x) ++rev;return rev;}template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // 最大値を更新(更新されたら trueを返す)template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新(更新されたら trueを返す)int digit(ll x, int d=10) { int rev=0; while (x > 0) { rev++; x /= d;}; return rev; } // xのd進数桁数/*** @brief std.hpp* @docs docs/std/std.md*/// line 6 "/Users/seekworser/.cpp_lib/competitive_library/atcoder/lazysegtree.hpp"// line 2 "/Users/seekworser/.cpp_lib/competitive_library/atcoder/internal_bit.hpp"#ifdef _MSC_VER#include <intrin.h>#endifnamespace atcoder {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 atcoder// line 8 "/Users/seekworser/.cpp_lib/competitive_library/atcoder/lazysegtree.hpp"namespace atcoder {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:S (*op)(S, S) = _op;S (*e)() = _e;S (*mapping)(F, S) = _mapping;F (*composition)(F, F) = _composition;F (*id)() = _id;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);}void add(int p, S x) {assert(0 <= p && p < _n);(*this).set(p, (*this).get(p) + x);}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) {assert(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) {assert(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) {assert(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) {assert(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;}int n() {return (*this)._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();}};} // namespace atcoder// line 4 "/Users/seekworser/.cpp_lib/competitive_library/competitive/data_structure/lazysegtree.hpp"template <typename S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S), F (*composition)(F, F), F (*id)()>std::ostream& operator<<(std::ostream& os, atcoder::lazy_segtree<S, op, e, F, mapping, composition, id> seg) {int n = seg.n();rep(i, n) { os << seg.get(i); if (i != n-1) os << " "; }return os;};namespace lsegtree_internal {template<typename T> struct AddNode {T value;ll size;AddNode() : value(T(0)), size(1) {};AddNode(T value, ll size) : value(value), size(size) {};friend ostream& operator<<(std::ostream& os, const AddNode<T> &n) { os << n.value; return os; };};template<typename T> T e_max() { return -INFL; }template<> int e_max() { return -INF; }template<typename T> T e_min() { return INFL; }template<> int e_min() { return INF; }template<typename T> AddNode<T> e_add() { return {0, 1}; }template<typename T> T op_max(T x, T y) { return x > y ? x : y; }template<typename T> T op_min(T x, T y) { return x < y ? x : y; }template<typename T> AddNode<T> op_add(AddNode<T> x, AddNode<T> y) { return {x.value + y.value, x.size + y.size}; }template<typename T> T id_radd(){ return 0; }template<typename T> T id_rupdate(){ return INFL; }template<> int id_rupdate(){ return INF; }template<typename T> AddNode<T> mapping_add_radd(T f, AddNode<T> x){ return {x.value + f * x.size, x.size}; }template<typename T> AddNode<T> mapping_add_rupdate(T f, AddNode<T> x){AddNode<T> rev = AddNode<T>(x);if(f != id_rupdate<T>()) rev.value = f * rev.size;return rev;}template<typename T> T mapping_radd(T f, T x){ return f+x; }template<typename T> T mapping_rupdate(T f, T x){ return (f == id_rupdate<T>() ? x : f); }template<typename T> T composition_radd(T f, T g){ return f+g; }template<typename T> T composition_rupdate(T f, T g){ return (f == id_rupdate<T>() ? g : f); }}template <typename S, S (*op)(S, S), S (*e)(), class F, S (*mapping)(F, S), F (*composition)(F, F), F (*id)()>using lsegtree = atcoder::lazy_segtree<S, op, e, F, mapping, composition, id>;template<typename T> using lseg_add_radd = atcoder::lazy_segtree<lsegtree_internal::AddNode<T>, lsegtree_internal::op_add<T>, lsegtree_internal::e_add<T>, T, lsegtree_internal::mapping_add_radd<T>, lsegtree_internal::composition_radd<T>, lsegtree_internal::id_radd<T>>;template<typename T> using lseg_min_radd = atcoder::lazy_segtree<T, lsegtree_internal::op_min<T>, lsegtree_internal::e_min<T>, T, lsegtree_internal::mapping_radd<T>, lsegtree_internal::composition_radd<T>, lsegtree_internal::id_radd<T>>;template<typename T> using lseg_max_radd = atcoder::lazy_segtree<T, lsegtree_internal::op_max<T>, lsegtree_internal::e_max<T>, T, lsegtree_internal::mapping_radd<T>, lsegtree_internal::composition_radd<T>, lsegtree_internal::id_radd<T>>;template<typename T> using lseg_add_rupdate = atcoder::lazy_segtree<lsegtree_internal::AddNode<T>, lsegtree_internal::op_add<T>, lsegtree_internal::e_add<T>, T, lsegtree_internal::mapping_add_rupdate<T>, lsegtree_internal::composition_rupdate<T>, lsegtree_internal::id_rupdate<T>>;template<typename T> using lseg_min_rupdate = atcoder::lazy_segtree<T, lsegtree_internal::op_min<T>, lsegtree_internal::e_min<T>, T,lsegtree_internal::mapping_rupdate<T>, lsegtree_internal::composition_rupdate<T>, lsegtree_internal::id_rupdate<T>>;template<typename T> using lseg_max_rupdate = atcoder::lazy_segtree<T, lsegtree_internal::op_max<T>, lsegtree_internal::e_max<T>, T,lsegtree_internal::mapping_rupdate<T>, lsegtree_internal::composition_rupdate<T>, lsegtree_internal::id_rupdate<T>>;/*** @brief 遅延セグメント木(ラッパー)* @docs docs/data_structure/lazysegtree.md*/// line 4 "/Users/seekworser/.cpp_lib/competitive_library/atcoder/modint.hpp"#include <type_traits>#ifdef _MSC_VER#include <intrin.h>#endif// line 3 "/Users/seekworser/.cpp_lib/competitive_library/atcoder/internal_math.hpp"#ifdef _MSC_VER#include <intrin.h>#endifnamespace atcoder {namespace internal {// @param m `1 <= m`// @return x mod mconstexpr long long safe_mod(long long x, long long m) {x %= m;if (x < 0) x += m;return x;}// Fast modular multiplication by barrett reduction// Reference: https://en.wikipedia.org/wiki/Barrett_reduction// NOTE: reconsider after Ice Lakestruct barrett {unsigned int _m;unsigned long long im;// @param m `1 <= m < 2^31`explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}// @return munsigned int umod() const { return _m; }// @param a `0 <= a < m`// @param b `0 <= b < m`// @return `a * b % m`unsigned int mul(unsigned int a, unsigned int b) const {// [1] m = 1// a = b = im = 0, so okay// [2] m >= 2// im = ceil(2^64 / m)// -> im * m = 2^64 + r (0 <= r < m)// let z = a*b = c*m + d (0 <= c, d < m)// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2// ((ab * im) >> 64) == c or c + 1unsigned 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;}};// @param n `0 <= n`// @param m `1 <= m`// @return `(x ** n) % m`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;}// Reference:// M. Forisek and J. Jancina,// Fast Primality Testing for Integers That Fit into a Machine Word// @param n `0 <= n`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;constexpr long long bases[3] = {2, 7, 61};for (long long a : bases) {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);// @param b `1 <= b`// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/gconstexpr 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};// Contracts:// [1] s - m0 * a = 0 (mod b)// [2] t - m1 * a = 0 (mod b)// [3] s * |m1| + t * |m0| <= blong 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 <= b// [3]:// (s - t * u) * |m1| + t * |m0 - m1 * u|// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)// = s * |m1| + t * |m0| <= bauto tmp = s;s = t;t = tmp;tmp = m0;m0 = m1;m1 = tmp;}// by [3]: |m0| <= b/g// by g != b: |m0| < b/gif (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);// @param n `n < 2^32`// @param m `1 <= m < 2^32`// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)unsigned long long floor_sum_unsigned(unsigned long long n,unsigned long long m,unsigned long long a,unsigned long long b) {unsigned long long ans = 0;while (true) {if (a >= m) {ans += n * (n - 1) / 2 * (a / m);a %= m;}if (b >= m) {ans += n * (b / m);b %= m;}unsigned long long y_max = a * n + b;if (y_max < m) break;// y_max < m * (n + 1)// floor(y_max / m) <= nn = (unsigned long long)(y_max / m);b = (unsigned long long)(y_max % m);std::swap(m, a);}return ans;}} // namespace internal} // namespace atcoder// line 5 "/Users/seekworser/.cpp_lib/competitive_library/atcoder/internal_type_traits.hpp"namespace atcoder {namespace internal {#ifndef _MSC_VERtemplate <class T>using is_signed_int128 =typename std::conditional<std::is_same<T, __int128_t>::value ||std::is_same<T, __int128>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int128 =typename std::conditional<std::is_same<T, __uint128_t>::value ||std::is_same<T, unsigned __int128>::value,std::true_type,std::false_type>::type;template <class T>using make_unsigned_int128 =typename std::conditional<std::is_same<T, __int128_t>::value,__uint128_t,unsigned __int128>;template <class T>using is_integral = typename std::conditional<std::is_integral<T>::value ||is_signed_int128<T>::value ||is_unsigned_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using is_signed_int = typename std::conditional<(is_integral<T>::value &&std::is_signed<T>::value) ||is_signed_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int =typename std::conditional<(is_integral<T>::value &&std::is_unsigned<T>::value) ||is_unsigned_int128<T>::value,std::true_type,std::false_type>::type;template <class T>using to_unsigned = typename std::conditional<is_signed_int128<T>::value,make_unsigned_int128<T>,typename std::conditional<std::is_signed<T>::value,std::make_unsigned<T>,std::common_type<T>>::type>::type;#elsetemplate <class T> using is_integral = typename std::is_integral<T>;template <class T>using is_signed_int =typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,std::true_type,std::false_type>::type;template <class T>using is_unsigned_int =typename std::conditional<is_integral<T>::value &&std::is_unsigned<T>::value,std::true_type,std::false_type>::type;template <class T>using to_unsigned = typename std::conditional<is_signed_int<T>::value,std::make_unsigned<T>,std::common_type<T>>::type;#endiftemplate <class T>using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;template <class T>using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;template <class T> using to_unsigned_t = typename to_unsigned<T>::type;} // namespace internal} // namespace atcoder// line 12 "/Users/seekworser/.cpp_lib/competitive_library/atcoder/modint.hpp"namespace atcoder {namespace internal {struct modint_base {};struct static_modint_base : modint_base {};template <class T> using is_modint = std::is_base_of<modint_base, T>;template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;} // namespace internaltemplate <int m, std::enable_if_t<(1 <= m)>* = nullptr>struct static_modint : internal::static_modint_base {using mint = static_modint;public:static constexpr int mod() { return m; }static mint raw(int v) {mint x;x._v = v;return x;}static_modint() : _v(0) {}template <class T, internal::is_signed_int_t<T>* = nullptr>static_modint(T v) {long long x = (long long)(v % (long long)(umod()));if (x < 0) x += umod();_v = (unsigned int)(x);}template <class T, internal::is_unsigned_int_t<T>* = nullptr>static_modint(T v) {_v = (unsigned int)(v % umod());}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;}mint& operator+=(const mint& rhs) {_v += rhs._v;if (_v >= umod()) _v -= umod();return *this;}mint& operator-=(const mint& rhs) {_v -= rhs._v;if (_v >= umod()) _v += umod();return *this;}mint& operator*=(const mint& rhs) {unsigned long long z = _v;z *= rhs._v;_v = (unsigned int)(z % umod());return *this;}mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }mint& operator=(const mint& rhs) { (*this)._v = rhs.val(); return *this; }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 {if (prime) {assert(_v);return pow(umod() - 2);} else {auto eg = internal::inv_gcd(_v, m);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;}private:unsigned int _v;static constexpr unsigned int umod() { return m; }static constexpr bool prime = internal::is_prime<m>;};template <int id> struct dynamic_modint : internal::modint_base {using mint = dynamic_modint;public:static int mod() { return (int)(bt.umod()); }static void set_mod(int m) {assert(1 <= m);bt = internal::barrett(m);}static mint raw(int v) {mint x;x._v = v;return x;}dynamic_modint() : _v(0) {}template <class T, internal::is_signed_int_t<T>* = nullptr>dynamic_modint(T v) {long long x = (long long)(v % (long long)(mod()));if (x < 0) x += mod();_v = (unsigned int)(x);}template <class T, internal::is_unsigned_int_t<T>* = nullptr>dynamic_modint(T v) {_v = (unsigned int)(v % mod());}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;}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 mint& rhs) { (*this)._v = rhs.val(); return *this; }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 = internal::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;}private:unsigned int _v;static internal::barrett bt;static unsigned int umod() { return bt.umod(); }};template <int id> internal::barrett dynamic_modint<id>::bt(998244353);using modint998244353 = static_modint<998244353>;using modint1000000007 = static_modint<1000000007>;using modint = dynamic_modint<-1>;namespace internal {template <class T>using is_static_modint = std::is_base_of<internal::static_modint_base, T>;template <class T>using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;template <class> struct is_dynamic_modint : public std::false_type {};template <int id>struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};template <class T>using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;} // namespace internal} // namespace atcoder// line 4 "/Users/seekworser/.cpp_lib/competitive_library/competitive/math/modint.hpp"namespace modint_internal {template<typename Mint> Mint pow(Mint a, ll n) {Mint res = 1;while (n > 0) {if (n & 1) res *= a;if (n > 1) a *= a;n >>= 1;}return res;}template<typename Mint> inline istream& input(istream& is, Mint& x) {ll a; is >> a; x = a; return is; }template<typename Mint> inline ostream& print(ostream& os, const Mint& x) { os << x.val(); return os; }}inline istream& operator>>(istream& is, atcoder::modint& x) { return modint_internal::input(is, x); }template<int m> inline istream& operator>>(istream& is, atcoder::static_modint<m>& x) { return modint_internal::input(is, x); }inline ostream& operator<<(ostream& os, const atcoder::modint& x) { return modint_internal::print(os, x); }template<int m> inline ostream& operator<<(ostream& os, const atcoder::static_modint<m>& x) { return modint_internal::print(os, x); }atcoder::modint pow(atcoder::modint a, ll n) { return modint_internal::pow(a, n); }template<int m> atcoder::static_modint<m> pow(atcoder::static_modint<m> a, ll n) { return modint_internal::pow(a, n); }using modint998244353 = atcoder::modint998244353;using modint1000000007 = atcoder::modint1000000007;using modint = atcoder::modint;/*** @brief modint.hpp* @docs docs/math/modint.md*/// line 3 "/Users/seekworser/.cpp_lib/competitive_library/competitive/data_structure/bit.hpp"template<typename T> struct Bit {vector<T> bit;int _n;Bit(int size, T val = T(0)) : _n(size), bit(size+1, val) {}Bit(const vector<T> val) : _n(sz(val)), bit(sz(val)+1, T(0)) {rep(i, _n) set(i, val[i]);}void add(int p, T x) {assert(0 <= p && p <= _n);p++;for (int i = p; i <= _n; i += i & -i) {bit[i] += x;}}T sum(int r) const {assert(0 <= r && r <= _n);T ret = 0;for (int i = r; i > 0; i -= i & -i){ret += bit[i];}return ret;}T sum(int l, int r) const {return sum(r) - sum(l);}T get(int p) const {assert(0 <= p && p < _n);return sum(p, p+1);}void set(int p, T x) {assert(0 <= p && p < _n);add(p, x - get(p));}int lower_bound(T w) const {if (w <= 0) return 0;int x = 0;for (int k = 1 << __lg(_n); k; k >>= 1) {if (x + k <= _n && bit[x + k] < w) {w -= bit[x + k];x += k;}}return x;}int upper_bound(T w) const {if (w < 0) return 0;int x = 0;for (int k = 1 << __lg(_n); k; k >>= 1) {if (x + k <= _n && bit[x + k] <= w) {w -= bit[x + k];x += k;}}return x;}};template <typename T> std::ostream& operator<<(std::ostream& os, const Bit<T> bit) {rep(i, bit._n) { os << bit.get(i); if (i != bit._n-1) os << " "; }return os;};/*** @brief BIT(Binary Index Tree)* @docs docs/data_structure/bit.md*/// line 4 "/Users/seekworser/.cpp_lib/competitive_library/competitive/math/inversion_num.hpp"template<class T> ll inversion_number(vector<T> &a) {ll ans = 0;Bit<ll> b(a.size());vector<T> sorted_a = a;sort(all(sorted_a));unordered_map<T, ll> ind_map;rep(i, a.size()) ind_map[sorted_a[i]] = i;rep(i, a.size()) {ans += i - b.sum(ind_map[a[i]] + 1);b.add(ind_map[a[i]], 1);}return ans;}/*** @brief inversion_num.hpp* @docs docs/math/inversion_num.md*/// line 4 "/Users/seekworser/.cpp_lib/competitive_library/competitive/math/combination.hpp"template<typename mint> struct Combination {vector<mint> fact, fact_inv;Combination(int nmax) : fact(nmax+1), fact_inv(nmax+1) {int p = mint::mod();vector<mint> inv(nmax+1);fact[0] = fact[1] = 1;fact_inv[0] = fact_inv[1] = 1;inv[0] = 0;inv[1] = 1;for (int i = 2; i < nmax+1; i++) {fact[i] = fact[i - 1] * i;inv[i] = p - inv[p % i] * (p / i);fact_inv[i] = fact_inv[i - 1] * inv[i];}}mint operator()(int n, int r) {if (r < 0 || n < r) return 0;return fact[n] * fact_inv[r] * fact_inv[n - r];}};/*** @brief combination.hpp* @docs docs/math/combination.md*/// line 3 "/Users/seekworser/.cpp_lib/competitive_library/competitive/std/io.hpp"// 演算子オーバーロード(プロトタイプ宣言)template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p);template <class T> inline istream& operator>>(istream& is, vector<T>& v);template <class T, class U> inline ostream& operator<<(ostream& os, const pair<T, U>& p);template <class T> inline ostream& operator<<(ostream& os, const vector<T>& v);template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp);template <typename T> ostream &operator<<(ostream &os, const set<T> &st);template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st);template <typename T> ostream &operator<<(ostream &os, const unordered_set<T> &st);template <typename T> ostream &operator<<(ostream &os, queue<T> q);template <typename T> ostream &operator<<(ostream &os, deque<T> q);template <typename T> ostream &operator<<(ostream &os, stack<T> st);template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq);// 演算子オーバーロードtemplate <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repe(x, v) is >> x; return is; }template <class T, class U> inline ostream& operator<<(ostream& os, const pair<T, U>& p) { os << p.first << " " << p.second; return os; }template <class T> inline ostream& operator<<(ostream& os, const vector<T>& v) { rep(i, sz(v)) { os << v.at(i); if (i != sz(v) - 1) os << " "; }return os; }template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp) { for (auto &[key, val] : mp) { os << key << ":" << val << ""; } return os; }template <typename T> ostream &operator<<(ostream &os, const set<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os <<*itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st) { auto itr = st.begin(); for (int i = 0; i < (int)st.size(); i++) { os<< *itr << (i + 1 != (int)st.size() ? " " : ""); itr++; } return os; }template <typename T> ostream &operator<<(ostream &os, const unordered_set<T> &st) { ll cnt = 0; for (auto &e : st) { os << e << (++cnt != (int)st.size() ? " " : ""); } return os; }template <typename T> ostream &operator<<(ostream &os, queue<T> q) { while (q.size()) { os << q.front() << " "; q.pop(); } return os; }template <typename T> ostream &operator<<(ostream &os, deque<T> q) { while (q.size()) { os << q.front() << " "; q.pop_front(); } return os; }template <typename T> ostream &operator<<(ostream &os, stack<T> st) { while (st.size()) { os << st.top() << " "; st.pop(); } return os; }template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq) { while (pq.size()) {os << pq.top() << " "; pq.pop(); } return os; }template <typename T> int print_sep_end(string sep, string end, const T& val) { (void)sep; cout << val << end; return 0; };template <typename T1, typename... T2> int print_sep_end(string sep, string end, const T1 &val, const T2 &...remain) {cout << val << sep;print_sep_end(sep, end, remain...);return 0;};template <typename... T> int print(const T &...args) { print_sep_end(" ", "\n", args...); return 0; };template <typename... T> void flush() { cout << flush; };template <typename... T> int print_and_flush(const T &...args) { print(args...); flush(); return 0; };#define debug(...) debug_func(0, #__VA_ARGS__, __VA_ARGS__) // debug printtemplate <typename T> void input(T &a) { cin >> a; };template <typename T1, typename... T2> void input(T1&a, T2 &...b) { cin >> a; input(b...); };#ifdef LOCAL_TESTtemplate <typename T> void debug_func(int i, const T name) { (void)i; (void)name; cerr << endl; }template <typename T1, typename T2, typename... T3> void debug_func(int i, const T1 &name, const T2 &a, const T3 &...b) {int scope = 0;for ( ; (scope != 0 || name[i] != ',') && name[i] != '\0'; i++ ) {cerr << name[i];if (name[i] == '(' || name[i] == '{') scope++;if (name[i] == ')' || name[i] == '}') scope--;}cerr << ":" << a << " ";debug_func(i + 1, name, b...);}template <typename T1, typename T2, typename... T3> void debug_func(int i, const T1 &name, T2 &a, T3 &...b) {int scope = 0;for ( ; (scope != 0 || name[i] != ',') && name[i] != '\0'; i++ ) {cerr << name[i];if (name[i] == '(' || name[i] == '{') scope++;if (name[i] == ')' || name[i] == '}') scope--;}cerr << ":" << a << " ";debug_func(i + 1, name, b...);}#endif#ifndef LOCAL_TESTtemplate <typename... T>void debug_func(T &...) {}template <typename... T>void debug_func(const T &...) {}#endif/*** @brief io.hpp* @docs docs/std/io.md*/// line 80 "answer.cpp"#endif