結果
| 問題 | No.2327 Inversion Sum |
| ユーザー |
👑  seekworser
|
| 提出日時 | 2023-05-28 15:18:39 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 139 ms / 2,000 ms |
| コード長 | 42,904 bytes |
| コンパイル時間 | 2,560 ms |
| コンパイル使用メモリ | 231,912 KB |
| 実行使用メモリ | 12,424 KB |
| 最終ジャッジ日時 | 2024-06-08 07:28:29 |
| 合計ジャッジ時間 | 4,701 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
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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 | 25 ms
11,428 KB |
| testcase_01 | AC | 125 ms
10,764 KB |
| testcase_02 | AC | 99 ms
12,424 KB |
| testcase_03 | AC | 19 ms
10,996 KB |
| testcase_04 | AC | 139 ms
10,660 KB |
| testcase_05 | AC | 21 ms
7,900 KB |
| testcase_06 | AC | 91 ms
9,800 KB |
| testcase_07 | AC | 53 ms
6,404 KB |
| testcase_08 | AC | 20 ms
5,376 KB |
| testcase_09 | AC | 126 ms
10,572 KB |
| testcase_10 | AC | 33 ms
5,852 KB |
| testcase_11 | AC | 8 ms
7,788 KB |
| testcase_12 | AC | 7 ms
7,548 KB |
| testcase_13 | AC | 5 ms
5,376 KB |
| testcase_14 | AC | 77 ms
8,176 KB |
| testcase_15 | AC | 131 ms
9,272 KB |
| testcase_16 | AC | 54 ms
11,788 KB |
| testcase_17 | AC | 12 ms
7,912 KB |
| testcase_18 | AC | 17 ms
5,376 KB |
| testcase_19 | AC | 40 ms
11,252 KB |
| testcase_20 | AC | 4 ms
5,376 KB |
| testcase_21 | AC | 4 ms
5,376 KB |
| testcase_22 | AC | 4 ms
5,376 KB |
| testcase_23 | AC | 4 ms
5,376 KB |
| testcase_24 | AC | 5 ms
5,376 KB |
| testcase_25 | AC | 4 ms
5,376 KB |
| testcase_26 | AC | 4 ms
5,376 KB |
| testcase_27 | AC | 4 ms
5,376 KB |
| testcase_28 | AC | 3 ms
5,376 KB |
| testcase_29 | AC | 4 ms
5,376 KB |
| testcase_30 | AC | 4 ms
5,376 KB |
| testcase_31 | AC | 4 ms
5,376 KB |
| testcase_32 | AC | 4 ms
5,376 KB |
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_TEST
using 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pow
ll 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Sqrt
ll 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>
#endif
namespace 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_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __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>
#endif
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr 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 Lake
struct 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 m
unsigned 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 + 1
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned 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/g
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};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
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 <= b
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
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);
// @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) <= n
n = (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_VER
template <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;
#else
template <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;
#endif
template <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 internal
template <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 print
template <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_TEST
template <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_TEST
template <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