結果
| 問題 |
No.1062 素敵なスコア
|
| ユーザー |
 ecottea
|
| 提出日時 | 2025-06-12 18:37:34 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,072 ms / 2,000 ms |
| コード長 | 50,430 bytes |
| コンパイル時間 | 8,046 ms |
| コンパイル使用メモリ | 307,132 KB |
| 実行使用メモリ | 86,656 KB |
| 最終ジャッジ日時 | 2025-06-12 18:38:05 |
| 合計ジャッジ時間 | 19,797 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 32 |
ソースコード
#ifndef HIDDEN_IN_VS // 折りたたみ用
// 警告の抑制
#define _CRT_SECURE_NO_WARNINGS
// ライブラリの読み込み
#include <bits/stdc++.h>
using namespace std;
// 型名の短縮
using ll = long long; using ull = unsigned long long; // -2^63 ～ 2^63 = 9e18（int は -2^31 ～ 2^31 = 2e9）
using pii = pair<int, int>; using pll = pair<ll, ll>; using pil = pair<int, ll>; using pli = pair<ll, int>;
using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>; using vvvvi = vector<vvvi>;
using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>; using vvvvl = vector<vvvl>;
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>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;
// 定数の定義
const double PI = acos(-1);
int DX[4] = { 1, 0, -1, 0 }; // 4 近傍（下，右，上，左）
int DY[4] = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004003094073385LL; // (int)INFL = INF, (int)(-INFL) = -INF;
// 入出力高速化
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;
// 汎用マクロの定義
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), (x)))
#define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), (x)))
#define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 から n-1 まで昇順
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s から t まで昇順
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s から t まで降順
#define repe(v, a) for(const auto& v : (a)) // a の全要素（変更不可能）
#define repea(v, a) for(auto& v : (a)) // a の全要素（変更可能）
#define repb(set, d) for(int set = 0, set##_ub = 1 << int(d); set < set##_ub; ++set) // d ビット全探索（昇順）
#define repis(i, set) for(int i = lsb(set), bset##i = set; i < 32; bset##i -= 1 << i, i = lsb(bset##i)) // set の全要素（昇順）
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a の順列全て（昇順）
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去
#define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了
#define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) // 半開矩形内判定
// 汎用関数の定義
template <class T> inline ll powi(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
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）
template <class T> inline T getb(T set, int i) { return (set >> i) & T(1); }
template <class T> inline T smod(T n, T m) { n %= m; if (n < 0) n += m; return n; } // 非負mod
// 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) { repea(x, v) is >> x; return is; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; }
#endif // 折りたたみ用
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#ifdef _MSC_VER
#include "localACL.hpp"
#endif
using mint = modint998244353;
//using mint = static_modint<(int)1e9 + 7>;
//using mint = modint; // mint::set_mod(m);
namespace atcoder {
inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
}
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>; using vvvvm = vector<vvvm>; using pim = pair<int, mint>;
#endif
#ifdef _MSC_VER // 手元環境（Visual Studio）
#include "local.hpp"
#else // 提出用（gcc）
int mute_dump = 0;
inline int popcount(int n) { return __builtin_popcount(n); }
inline int popcount(ll n) { return __builtin_popcountll(n); }
inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : 32; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : 64; }
inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; }
inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; }
#define dump(...)
#define dumpel(v)
#define dump_math(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) { vc MLE(1<<30); EXIT(MLE.back()); } } // RE の代わりに MLE を出す
#endif
// 順列全探索
mint naive(int n, int a1, int a2) {
mint res = 0;
vi p0(n);
iota(all(p0), 1);
repp(p0) {
vi p1(p0);
{
int k = a1;
auto& p = p1;
int l = 0, r = n - 1;
while (1) {
while (l < n && p[l] <= k) l++;
while (r >= 0 && p[r] > k) r--;
if (l > r) break;
swap(p[l], p[r]);
}
}
vi p2(p0);
{
int k = a2;
auto& p = p2;
int l = 0, r = n - 1;
while (1) {
while (l < n && p[l] <= k) l++;
while (r >= 0 && p[r] > k) r--;
if (l > r) break;
swap(p[l], p[r]);
}
}
int sc = 0;
rep(i, n) sc += p1[i] == p2[i];
dump(p0, ":", "p1:", p1, "p2:", p2, "sc:", sc);
res += sc;
}
return res;
}
// これでは項数が足りなかった
void zikken() {
int N = 10;
vvvm tbl(N);
repi(n, 2, N) {
tbl[n - 1].resize(n - 1);
repi(a2, 1, n - 1) {
tbl[n - 1][a2 - 1].resize(a2 - 1);
repi(a1, 1, a2 - 1) {
auto val = naive(n, a1, a2);
tbl[n - 1][a2 - 1][a1 - 1] = val;
//dump(n, a2, a1, ":", val);
}
}
dump("---------------- n:", n, "-----------------");
dumpel(tbl[n - 1]);
}
dump_math(tbl);
exit(0);
}
/*
---------------- n: 2 -----------------
0:
---------------- n: 3 -----------------
0:
1: 8
---------------- n: 4 -----------------
0:
1: 48
2: 40 48
---------------- n: 5 -----------------
0:
1: 336
2: 248 312
3: 276 248 336
---------------- n: 6 -----------------
0:
1: 2640
2: 1920 2400
3: 1800 1760 2400
4: 2208 1800 1920 2640
---------------- n: 7 -----------------
0:
1: 23040
2: 17040 20880
3: 14760 15120 20160
4: 15696 13680 15120 20880
5: 19680 15696 14760 17040 23040
---------------- n: 8 -----------------
0:
1: 221760
2: 168000 201600
3: 141120 147840 191520
4: 137088 126000 141120 191520
5: 154560 129024 126000 147840 201600
6: 192960 154560 137088 141120 168000 221760
---------------- n: 9 -----------------
0:
1: 2338560
2: 1814400 2136960
3: 1512000 1599360 2016000
4: 1395072 1330560 1491840 1975680
5: 1451520 1266048 1270080 1491840 2016000
6: 1676160 1384320 1266048 1330560 1599360 2136960
7: 2066400 1676160 1451520 1395072 1512000 1814400 2338560
---------------- n: 10 -----------------
0:
1: 26853120
2: 21288960 24675840
3: 17781120 18869760 23224320
4: 15966720 15603840 17418240 22498560
5: 15724800 14224896 14515200 16934400 22498560
6: 17003520 14515200 13644288 14515200 17418240 23224320
7: 19776960 16381440 14515200 14224896 15603840 18869760 24675840
8: 24030720 19776960 17003520 15724800 15966720 17781120 21288960 26853120
*/
//【階乗など（法が大きな素数）】
/*
* Factorial_mint(int N) : O(n)
* N まで計算可能として初期化する．
*
* mint fact(int n) : O(1)
* n! を返す．
*
* mint fact_inv(int n) : O(1)
* 1/n! を返す（n が負なら 0 を返す）
*
* mint inv(int n) : O(1)
* 1/n を返す．
*
* mint perm(int n, int r) : O(1)
* 順列の数 nPr を返す．
*
* mint perm_inv(int n, int r) : O(1)
* 順列の数の逆数 1/nPr を返す．
*
* mint bin(int n, int r) : O(1)
* 二項係数 nCr を返す．
*
* mint bin_inv(int n, int r) : O(1)
* 二項係数の逆数 1/nCr を返す．
*
* mint mul(vi rs) : O(|rs|)
* 多項係数 nC[rs] を返す．（n = Σrs）
*
* mint hom(int n, int r) : O(1)
* 重複組合せの数 nHr = n+r-1Cr を返す（0H0 = 1 とする）
*
* mint neg_bin(int n, int r) : O(1)
* 負の二項係数 nCr = (-1)^r -n+r-1Cr を返す（n ≦ 0, r ≧ 0）
*
* mint pochhammer(int x, int n) : O(1)
* ポッホハマー記号 x^(n) を返す（n ≧ 0）
*
* mint pochhammer_inv(int x, int n) : O(1)
* ポッホハマー記号の逆数 1/x^(n) を返す（n ≧ 0）
*/
class Factorial_mint {
int n_max;
// 階乗と階乗の逆数の値を保持するテーブル
vm fac, fac_inv;
public:
// n! までの階乗とその逆数を前計算しておく．O(n)
Factorial_mint(int n) : n_max(n), fac(n + 1), fac_inv(n + 1) {
// verify : https://atcoder.jp/contests/dwacon6th-prelims/tasks/dwacon6th_prelims_b
fac[0] = 1;
repi(i, 1, n) fac[i] = fac[i - 1] * i;
fac_inv[n] = fac[n].inv();
repir(i, n - 1, 0) fac_inv[i] = fac_inv[i + 1] * (i + 1);
}
Factorial_mint() : n_max(0) {} // ダミー
// n! を返す．
mint fact(int n) const {
// verify : https://atcoder.jp/contests/dwacon6th-prelims/tasks/dwacon6th_prelims_b
Assert(0 <= n && n <= n_max);
return fac[n];
}
// 1/n! を返す（n が負なら 0 を返す）
mint fact_inv(int n) const {
// verify : https://atcoder.jp/contests/abc289/tasks/abc289_h
Assert(n <= n_max);
if (n < 0) return 0;
return fac_inv[n];
}
// 1/n を返す．
mint inv(int n) const {
// verify : https://atcoder.jp/contests/exawizards2019/tasks/exawizards2019_d
Assert(n > 0);
Assert(n <= n_max);
return fac[n - 1] * fac_inv[n];
}
// 順列の数 nPr を返す．
mint perm(int n, int r) const {
// verify : https://atcoder.jp/contests/abc172/tasks/abc172_e
Assert(n <= n_max);
if (r < 0 || n - r < 0) return 0;
return fac[n] * fac_inv[n - r];
}
// 順列の数 nPr の逆数を返す．
mint perm_inv(int n, int r) const {
// verify : https://yukicoder.me/problems/no/3139
Assert(n <= n_max);
Assert(0 <= r); Assert(r <= n);
return fac_inv[n] * fac[n - r];
}
// 二項係数 nCr を返す．
mint bin(int n, int r) const {
// verify : https://judge.yosupo.jp/problem/binomial_coefficient_prime_mod
Assert(n <= n_max);
if (r < 0 || n - r < 0) return 0;
return fac[n] * fac_inv[r] * fac_inv[n - r];
}
// 二項係数の逆数 1/nCr を返す．
mint bin_inv(int n, int r) const {
// verify : https://www.codechef.com/problems/RANDCOLORING
Assert(n <= n_max);
Assert(r >= 0);
Assert(n - r >= 0);
return fac_inv[n] * fac[r] * fac[n - r];
}
// 多項係数 nC[rs] を返す．
mint mul(const vi& rs) const {
// verify : https://yukicoder.me/problems/no/2141
if (*min_element(all(rs)) < 0) return 0;
int n = accumulate(all(rs), 0);
Assert(n <= n_max);
mint res = fac[n];
repe(r, rs) res *= fac_inv[r];
return res;
}
// 重複組合せの数 nHr = n+r-1Cr を返す（0H0 = 1 とする）
mint hom(int n, int r) {
// verify : https://mojacoder.app/users/riantkb/problems/toj_ex_2
if (n == 0) return (int)(r == 0);
if (r < 0 || n - 1 < 0) return 0;
Assert(n + r - 1 <= n_max);
return fac[n + r - 1] * fac_inv[r] * fac_inv[n - 1];
}
// 負の二項係数 nCr を返す（n ≦ 0, r ≧ 0）
mint neg_bin(int n, int r) {
// verify : https://atcoder.jp/contests/abc345/tasks/abc345_g
if (n == 0) return (int)(r == 0);
if (r < 0 || -n - 1 < 0) return 0;
Assert(-n + r - 1 <= n_max);
return (r & 1 ? -1 : 1) * fac[-n + r - 1] * fac_inv[r] * fac_inv[-n - 1];
}
// ポッホハマー記号 x^(n) を返す（n ≧ 0）
mint pochhammer(int x, int n) {
// verify : https://atcoder.jp/contests/agc070/tasks/agc070_c
int x2 = x + n - 1;
if (x <= 0 && 0 <= x2) return 0;
if (x > 0) {
Assert(x2 <= n_max);
return fac[x2] * fac_inv[x - 1];
}
else {
Assert(-x <= n_max);
return (n & 1 ? -1 : 1) * fac[-x] * fac_inv[-x2 - 1];
}
}
// ポッホハマー記号の逆数 1/x^(n) を返す（n ≧ 0）
mint pochhammer_inv(int x, int n) {
// verify : https://atcoder.jp/contests/agc070/tasks/agc070_c
int x2 = x + n - 1;
Assert(!(x <= 0 && 0 <= x2));
if (x > 0) {
Assert(x2 <= n_max);
return fac_inv[x2] * fac[x - 1];
}
else {
Assert(-x <= n_max);
return (n & 1 ? -1 : 1) * fac_inv[-x] * fac[-x2 - 1];
}
}
};
Factorial_mint fm(100010);
// とりあえず多項式オーダーにした
mint TLE(int n, int a1, int a2) {
if (a1 == a2) return fm.fact(n) * n;
if (a1 > a2) swap(a1, a2);
int cL = a1;
int cM = a2 - a1;
int cR = n - a2;
dump(cL, cM, cR);
mint res = 0;
dump("a2 より大，不動 :");
repi(i, 1, n) {
repi(cLl, 0, cL) repi(cMl, 0, cM) {
int cLr = cL - cLl;
int cMr = cM - cMl;
int cRl = (i - 1) - cLl - cMl;
int cRr = (n - i) - cLr - cMr;
if (cRl < 0 || cRr < 0) continue;
if (cMl + cRl < cLr) continue;
if (cRl < cLr + cMr) continue;
mint pos = fm.mul({ cLl, cMl, cRl }) * fm.mul({ cLr, cMr, cRr });
mint val = fm.fact(cL) * fm.fact(cM) * fm.fact(cR - 1);
dump("i:", i, "c:", cLl, cMl, cRl, cLr, cMr, cRr, ":", pos, val);
res += pos * val * cR;
}
}
dump("a2 より大，移動 :");
repi(i, 1, n) repi(j, i + 1, n) {
repi(cLl, 0, cL) {
int cMl = 0;
int cRl = (i - 1) - cLl - cMl;
int cLr = cRl;
int cMr = 0;
int cRr = (n - j) - cLr - cMr;
int cLm = (cL - 1) - cLl - cLr;
int cMm = cM - cMl - cMr;
int cRm = (cR - 1) - cRl - cRr;
if (cRl < 0 || cRr < 0 || cLm < 0 || cMm < 0 || cRm < 0) continue;
mint pos = fm.mul({ cLl, cMl, cRl }) * fm.mul({ cLm, cMm, cRm }) * fm.mul({ cLr, cMr, cRr });
mint val = fm.fact(cL - 1) * fm.fact(cM) * fm.fact(cR - 1);
dump("i:", i, "j:", j, "c:", cLl, cMl, cRl, cLm, cMm, cRm, cLr, cMr, cRr, ":", pos, val);
res += pos * val * cL * cR;
}
}
dump("a1 より大，a2 以下，不動 :");
repi(i, 1, n) {
repi(cLl, 0, cL) repi(cMl, 0, cM - 1) {
int cLr = cL - cLl;
int cMr = (cM - 1) - cMl;
int cRl = (i - 1) - cLl - cMl;
int cRr = (n - i) - cLr - cMr;
if (cRl < 0 || cRr < 0) continue;
if (cMl + cRl < cLr) continue;
if (cRl > cLr + cMr) continue;
mint pos = fm.mul({ cLl, cMl, cRl }) * fm.mul({ cLr, cMr, cRr });
mint val = fm.fact(cL) * fm.fact(cM - 1) * fm.fact(cR);
dump("i:", i, "c:", cLl, cMl, cRl, cLr, cMr, cRr, ":", pos, val);
res += pos * val * cM;
}
}
{
swap(a1, a2);
a1 = n - a1;
a2 = n - a2;
dump(a1, a2);
cL = a1;
cM = a2 - a1;
cR = n - a2;
dump("a2 より大，不動 :");
repi(i, 1, n) {
repi(cLl, 0, cL) repi(cMl, 0, cM) {
int cLr = cL - cLl;
int cMr = cM - cMl;
int cRl = (i - 1) - cLl - cMl;
int cRr = (n - i) - cLr - cMr;
if (cRl < 0 || cRr < 0) continue;
if (cMl + cRl < cLr) continue;
if (cRl < cLr + cMr) continue;
mint pos = fm.mul({ cLl, cMl, cRl }) * fm.mul({ cLr, cMr, cRr });
mint val = fm.fact(cL) * fm.fact(cM) * fm.fact(cR - 1);
dump("i:", i, "c:", cLl, cMl, cRl, cLr, cMr, cRr, ":", pos, val);
res += pos * val * cR;
}
}
dump("a2 より大，移動 :");
repi(i, 1, n) repi(j, i + 1, n) {
repi(cLl, 0, cL) {
int cMl = 0;
int cRl = (i - 1) - cLl - cMl;
int cLr = cRl;
int cMr = 0;
int cRr = (n - j) - cLr - cMr;
int cLm = (cL - 1) - cLl - cLr;
int cMm = cM - cMl - cMr;
int cRm = (cR - 1) - cRl - cRr;
if (cRl < 0 || cRr < 0 || cLm < 0 || cMm < 0 || cRm < 0) continue;
mint pos = fm.mul({ cLl, cMl, cRl }) * fm.mul({ cLm, cMm, cRm }) * fm.mul({ cLr, cMr, cRr });
mint val = fm.fact(cL - 1) * fm.fact(cM) * fm.fact(cR - 1);
dump("i:", i, "j:", j, "c:", cLl, cMl, cRl, cLm, cMm, cRm, cLr, cMr, cRr, ":", pos, val);
res += pos * val * cL * cR;
}
}
}
return res;
}
void bug_find() {
#ifdef _MSC_VER
// 合わない入力例を見つける．
mute_dump = true;
mt19937_64 mt((int)time(NULL));
uniform_int_distribution<ll> rnd(0LL, 1LL << 60);
rep(hoge, 100) {
int n = rnd(mt) % 7 + 2;
int a1 = rnd(mt) % (n - 1) + 1;
int a2 = rnd(mt) % (n - 1) + 1;
auto res_naive = naive(n, a1, a2);
auto res_solve = TLE(n, a1, a2);
if (res_naive != res_solve) {
cout << "----------error!----------" << endl;
cout << "input:" << endl;
cout << n << " " << a1 << " " << a2 << endl;
cout << "results:" << endl;
cout << res_naive << endl;
cout << res_solve << endl;
cout << "--------------------------" << endl;
}
}
mute_dump = false;
exit(0);
#endif
}
// これで項数が足りた
void zikken2() {
int N = 20;
vvvm tbl(N);
repi(n, 2, N) {
tbl[n - 1].resize(n - 1);
repi(a2, 1, n - 1) {
tbl[n - 1][a2 - 1].resize(a2 - 1);
repi(a1, 1, a2 - 1) {
mute_dump = 1;
auto val = TLE(n, a1, a2);
mute_dump = 0;
tbl[n - 1][a2 - 1][a1 - 1] = val;
//dump(n, a2, a1, ":", val);
}
}
dump("---------------- n:", n, "-----------------");
dumpel(tbl[n - 1]);
}
dump_math(tbl);
exit(0);
}
//【行列】
/*
* Matrix<T>(int n, int m) : O(n m)
* n×m 零行列で初期化する．
*
* Matrix<T>(int n) : O(n^2)
* n×n 単位行列で初期化する．
*
* Matrix<T>(vvT a) : O(n m)
* 二次元配列 a[0..n)[0..m) の要素で初期化する．
*
* bool empty() : O(1)
* 行列が空かを返す．
*
* A + B : O(n m)
* n×m 行列 A, B の和を返す．+= も使用可．
*
* A - B : O(n m)
* n×m 行列 A, B の差を返す．-= も使用可．
*
* c * A ／ A * c : O(n m)
* n×m 行列 A とスカラー c のスカラー積を返す．*= も使用可．
*
* A * x : O(n m)
* n×m 行列 A と n 次元列ベクトル x の積を返す．
*
* x * A : O(n m)（やや遅い）
* m 次元行ベクトル x と n×m 行列 A の積を返す．
*
* A * B : O(n m l)
* n×m 行列 A と m×l 行列 B の積を返す．
*
* Mat pow(ll d) : O(n^3 log d)
* 自身を d 乗した行列を返す．
*/
template <class T>
struct Matrix {
int n, m; // 行列のサイズ（n 行 m 列）
vector<vector<T>> v; // 行列の成分
// n×m 零行列で初期化する．
Matrix(int n, int m) : n(n), m(m), v(n, vector<T>(m)) {}
// n×n 単位行列で初期化する．
Matrix(int n) : n(n), m(n), v(n, vector<T>(n)) { rep(i, n) v[i][i] = T(1); }
// 二次元配列 a[0..n)[0..m) の要素で初期化する．
Matrix(const vector<vector<T>>& a) : n(sz(a)), m(sz(a[0])), v(a) {}
Matrix() : n(0), m(0) {}
// 代入
Matrix(const Matrix&) = default;
Matrix& operator=(const Matrix&) = default;
// アクセス
inline vector<T> const& operator[](int i) const { return v[i]; }
inline vector<T>& operator[](int i) {
// verify : https://judge.yosupo.jp/problem/matrix_product
// inline を付けて [] でアクセスするとなぜか v[] への直接アクセスより速くなった．
return v[i];
}
// 入力
friend istream& operator>>(istream& is, Matrix& a) {
rep(i, a.n) rep(j, a.m) is >> a.v[i][j];
return is;
}
// 行の追加
void push_back(const vector<T>& a) {
Assert(sz(a) == m);
v.push_back(a);
n++;
}
// 行の削除
void pop_back() {
Assert(n > 0);
v.pop_back();
n--;
}
// サイズ変更
void resize(int n_) {
v.resize(n_);
n = n_;
}
void resize(int n_, int m_) {
n = n_;
m = m_;
v.resize(n);
rep(i, n) v[i].resize(m);
}
// 空か
bool empty() const { return min(n, m) == 0; }
// 比較
bool operator==(const Matrix& b) const { return n == b.n && m == b.m && v == b.v; }
bool operator!=(const Matrix& b) const { return !(*this == b); }
// 加算，減算，スカラー倍
Matrix& operator+=(const Matrix& b) {
rep(i, n) rep(j, m) v[i][j] += b[i][j];
return *this;
}
Matrix& operator-=(const Matrix& b) {
rep(i, n) rep(j, m) v[i][j] -= b[i][j];
return *this;
}
Matrix& operator*=(const T& c) {
rep(i, n) rep(j, m) v[i][j] *= c;
return *this;
}
Matrix operator+(const Matrix& b) const { return Matrix(*this) += b; }
Matrix operator-(const Matrix& b) const { return Matrix(*this) -= b; }
Matrix operator*(const T& c) const { return Matrix(*this) *= c; }
friend Matrix operator*(const T& c, const Matrix<T>& a) { return a * c; }
Matrix operator-() const { return Matrix(*this) *= T(-1); }
// 行列ベクトル積 : O(m n)
vector<T> operator*(const vector<T>& x) const {
vector<T> y(n);
rep(i, n) rep(j, m) y[i] += v[i][j] * x[j];
return y;
}
// ベクトル行列積 : O(m n)
friend vector<T> operator*(const vector<T>& x, const Matrix& a) {
vector<T> y(a.m);
rep(i, a.n) rep(j, a.m) y[j] += x[i] * a[i][j];
return y;
}
// 積：O(n^3)
Matrix operator*(const Matrix& b) const {
// verify : https://judge.yosupo.jp/problem/matrix_product
Matrix res(n, b.m);
rep(i, res.n) rep(k, m) rep(j, res.m) res[i][j] += v[i][k] * b[k][j];
return res;
}
Matrix& operator*=(const Matrix& b) { *this = *this * b; return *this; }
// 累乗：O(n^3 log d)
Matrix pow(ll d) const {
// verify : https://judge.yosupo.jp/problem/pow_of_matrix
Matrix res(n), pow2 = *this;
while (d > 0) {
if (d & 1) res *= pow2;
pow2 *= pow2;
d >>= 1;
}
return res;
}
#ifdef _MSC_VER
friend ostream& operator<<(ostream& os, const Matrix& a) {
rep(i, a.n) {
os << "[";
rep(j, a.m) os << a[i][j] << " ]"[j == a.m - 1];
if (i < a.n - 1) os << "\n";
}
return os;
}
#endif
};
//【線形方程式】O(n m min(n, m))
/*
* 与えられた n×m 行列 A と n 次元ベクトル b に対し，
* 線形方程式 A x = b の特殊解 x0（m 次元ベクトル）を返す（なければ空リスト）
* また同次形 A x = 0 の解空間の基底（m 次元ベクトル）のリストを xs に格納する．
*/
template <class T>
vector<T> gauss_jordan_elimination(const Matrix<T>& A, const vector<T>& b, vector<vector<T>>* xs = nullptr) {
// verify : https://judge.yosupo.jp/problem/system_of_linear_equations
int n = A.n, m = A.m;
// v : 拡大係数行列 (A | b)
vector<vector<T>> v(n, vector<T>(m + 1));
rep(i, n) rep(j, m) v[i][j] = A[i][j];
rep(i, n) v[i][m] = b[i];
// pivots[i] : 第 i 行のピボットが第何列にあるか
vi pivots;
// 注目位置を v[i][j] とする．
int i = 0, j = 0;
while (i < n && j <= m) {
// 注目列の下方の行から非 0 成分を見つける．
int i2 = i;
while (i2 < n && v[i2][j] == T(0)) i2++;
// 見つからなかったら注目位置を右に移す．
if (i2 == n) { j++; continue; }
// 見つかったら第 i 行とその行を入れ替える．
if (i != i2) swap(v[i], v[i2]);
// v[i][j] をピボットに選択する．
pivots.push_back(j);
// v[i][j] が 1 になるよう第 i 行全体を v[i][j] で割る．
T vij_inv = T(1) / v[i][j];
repi(j2, j, m) v[i][j2] *= vij_inv;
// 第 i 行以外の第 j 列の成分が全て 0 になるよう第 i 行を定数倍して減じる．
rep(i2, n) {
if (v[i2][j] == T(0) || i2 == i) continue;
T mul = v[i2][j];
repi(j2, j, m) v[i2][j2] -= v[i][j2] * mul;
}
// 注目位置を右下に移す．
i++; j++;
}
// 最後に見つかったピボットの位置が第 m 列ならば解なし．
if (!pivots.empty() && pivots.back() == m) return vector<T>();
// A x = b の特殊解 x0 の構成（任意定数は全て 0 にする）
vector<T> x0(m);
int rnk = sz(pivots);
rep(i, rnk) x0[pivots[i]] = v[i][m];
// 同次形 A x = 0 の一般解 {x} の基底の構成（任意定数を 1-hot にする）
if (xs != nullptr) {
xs->clear();
int i = 0;
rep(j, m) {
if (i < rnk && j == pivots[i]) {
i++;
continue;
}
vector<T> x(m);
x[j] = T(1);
rep(i2, i) x[pivots[i2]] = -v[i2][j];
xs->emplace_back(move(x));
}
}
return x0;
}
//【変数係数線形漸化式の発見】O(n L^2 D^2 + N (L D + log(mod)))
/*
* 係数多項式の次数が D 次未満の L 項間漸化式
* Σi∈[0..L) Σj∈[0..D) c(i,j) (m+i)^j a[m+i] = 0
* の存在を仮定して a[0..n) を延長し a[0..N] にする（失敗したら false を返す）
*
* 制約 : n ≧ L(D+1)-1（ランク落ちしてるとこれでも足りないかも）
*
* 利用：【行列】,【線形方程式】
*/
bool p_recursive(int N, vm& a, int L, int D, vm* coef = nullptr) {
// verify : https://atcoder.jp/contests/abc222/tasks/abc222_h
int n = sz(a);
// 既に十分な長さがある場合はそのままで良い．
if (N <= n - 1) {
a.resize(N + 1);
return true;
}
// 式が足りないといつでも非自明解をもってしまって意味がない（とも限らない）
if (n < L * (D + 1) - 1) return false;
// 行列方程式 A x = 0 を解いて一般解の基底 xs を求める．
Matrix<mint> A(n - L + 1, L * D);
repi(n0, 0, n - L) {
rep(i, L) rep(j, D) {
A[n0][i * D + j] = mint(n0 + i).pow(j) * a[n0 + i];
}
}
vvm xs;
gauss_jordan_elimination(A, vm(n - L + 1), &xs);
// 自明解 x = 0 しか存在しない場合は失敗．
if (xs.empty()) return false;
a.resize(N + 1);
// 得られた非自明解 xs.back() から漸化式を復元し，それに基づき a[0..n) を延長する．
auto& x = xs.back();
repi(n0, n - L + 1, N - L + 1) {
mint num = 0;
rep(i, L - 1) {
mint pow_n0i = 1;
rep(j, D) {
num += x[i * D + j] * pow_n0i * a[n0 + i];
pow_n0i *= n0 + i;
}
}
mint dnm = 0;
mint pow_n0L = 1;
rep(j, D) {
dnm += x[(L - 1) * D + j] * pow_n0L;
pow_n0L *= n0 + L - 1;
}
//dump("n0:", n0, "dnm:", dnm);
//if (dnm != n0 + 2) exit(12345);
// num + dnm * a[n0 + L - 1] = 0
a[n0 + L - 1] = -num / dnm;
}
if (coef) *coef = move(x);
return true;
}
//【変数係数線形漸化式の発見】O(n L^2 D^2 + N (L D + log(mod)))（の改変）
/*
* 係数多項式の次数が D 次未満の L 項間漸化式
* Σi∈[0..L) Σj∈[0..D) c(i,j) (m+i)^j a[m+i] = 0
* の存在を仮定して a[0..n) を延長し a[0..N] にする（失敗したら false を返す）
*
* 制約 : n ≧ L(D+1)-1（ランク落ちしてるとこれでも足りないかも）
*
* 利用：【行列】,【線形方程式】
*/
bool p_recursive_edited(int N, vm& a, int L, int D, vm* coef = nullptr) {
// verify : https://atcoder.jp/contests/abc222/tasks/abc222_h
int n = sz(a);
// 既に十分な長さがある場合はそのままで良い．
if (N <= n - 1) {
a.resize(N + 1);
return true;
}
// 式が足りないといつでも非自明解をもってしまって意味がない（とも限らない）
if (n < L * (D + 1) - 1) return false;
// 行列方程式 A x = 0 を解いて一般解の基底 xs を求める．
Matrix<mint> A(n - L + 1, L * D);
repi(n0, 0, n - L) {
rep(i, L) rep(j, D) {
A[n0][i * D + j] = mint(n0 + i).pow(j) * a[n0 + i];
}
}
vvm xs;
gauss_jordan_elimination(A, vm(n - L + 1), &xs);
// 自明解 x = 0 しか存在しない場合は失敗．
if (xs.empty()) return false;
a.resize(N + 1);
// 得られた非自明解 xs.back() から漸化式を復元し，それに基づき a[0..n) を延長する．
auto& x = xs.back();
repi(n0, n - L + 1, N - L + 1) {
mint num = 0;
rep(i, L - 1) {
mint pow_n0i = 1;
rep(j, D) {
num += x[i * D + j] * pow_n0i * a[n0 + i];
pow_n0i *= n0 + i;
}
}
// num + dnm * a[n0 + L - 1] = 0
a[n0 + L - 1] = -num * fm.inv(n0 + 2); // 除算回避
}
if (coef) *coef = move(x);
return true;
}
// 埋め込み
vvvm seq012 = { {{8,48,336,2640,23040,221760,2338560,26853120,333849600,477704188,298575808},{40,248,1920,17040,168000,1814400,21288960,269740800,677612541,581561291,728382657},{276,1800,14760,141120,1512000,17781120,226800000,118777341,823656915,366190899,764061040},{2208,15696,137088,1395072,15966720,201035520,749787134,402160600,776637831,125157049,328394580},{19680,154560,1451520,15724800,191116800,558186494,107749339,52024766,476777082,331909681,186765417},{192960,1676160,17003520,196473600,535376894,849710045,939924956,108012740,462321415,26658156,909631924},{2066400,19776960,216820800,677936894,587075292,821147615,659020706,9539179,37634655,657301310,731993243},{24030720,252000000,983965694,293379033,347991496,933594392,797388978,279162056,212424334,651029171,744643915},{301916160,454078461,952039381,311133592,812956457,925433356,387622903,17597259,378009409,100824488,946766598},{85793788,557132750,578485583,312270807,636294809,494622216,445221739,854912,238722275,44733988,337723580},{100613573,63744236,107142948,757217903,687896675,79824955,576424003,334127970,765487456,521420866,414261348},{702434417,281359633,632301980,797822977,859409218,993475177,123587239,571219047,929706468,320442670,820192364},{181736862,791290923,845847956,175284481,600870838,559769104,501335516,471664524,473856220,67794608,770277444},{557869603,315302302,706335400,385201800,411358432,652572248,277229151,908633511,659015078,779598208,453977857}},{{48,312,2400,20880,201600,2136960,24675840,308448000,158369788,978783173,219540581},{248,1760,15120,147840,1599360,18869760,240710400,305055741,463432656,872459532,640849662},{1800,13680,126000,1330560,15603840,199584000,757770494,785361880,510267774,787222027,261485062},{15696,129024,1266048,14224896,177811200,430452734,794967005,911109581,280216343,698970372,210868062},{154560,1384320,14515200,172972800,292074494,109046751,671211005,607708789,9539179,373562499,99915770},{1676160,16381440,184032000,330090494,559860704,472411665,838690887,771134575,254486594,525190124,494646276},{19776960,210470400,538228094,68805598,156509194,507658398,279750694,90361170,826064156,655585639,684284705},{252000000,913002494,586750939,79277545,908822405,582475310,345445913,29687635,742245296,822680425,220001495},{454078461,89836501,853478831,223274240,112476899,100403411,746732352,716181067,171057347,31395043,245915766},{557132750,237317466,742007061,322916994,131443065,464058516,8431554,73923055,556084758,189892197,715009442},{63744236,997616581,518829362,956037809,168224541,568925982,762119703,769517696,618146626,811735202,386700995},{281359633,219083534,552009294,81504243,292154131,936488574,115964027,756646361,390013543,748630541,870256045},{791290923,897496481,933089978,98487844,809909845,765387923,337723580,363519834,875288630,611240272,29670571},{315302302,129890501,596316849,937793387,382668655,429531394,537137573,340236154,877540562,962556769,16604148}},{{336,2400,20160,191520,2016000,23224320,290304000,917113341,620505032,315591831,384133134},{1920,15120,141120,1491840,17418240,221356800,38943741,624397268,651771206,104569505,976650685},{14760,126000,1270080,14515200,183254400,518269694,187582939,368764342,805236128,570298222,858621105},{137088,1266048,13644288,166199040,238852094,724089824,8916478,895632990,987195988,490057561,676360669},{1451520,14515200,166924800,159018494,708771810,85757478,843837773,266883479,851597236,260642290,916227929},{17003520,184032000,261661694,914058210,391552561,993061534,421290059,924480099,669843992,333043594,926964610},{216820800,538228094,228797151,323312160,17543272,459891704,698448311,453514114,817989581,503005563,576441541},{983965694,586750939,987950581,397314235,54229368,389635151,469586766,61974125,217879253,941820993,850206792},{952039381,853478831,26713501,205120847,327369457,234578061,672519579,972415256,761347899,794630309,372531232},{578485583,742007061,551205840,448975666,76062841,678978884,526634671,440475659,851324507,375153521,73656597},{107142948,518829362,47173834,212424334,764076040,49203172,915002775,690690946,677217376,415962258,60180067},{632301980,552009294,487698820,939737961,425985022,145208798,775638335,691752786,27475110,341848174,118978583},{845847956,933089978,929271199,435858039,524521626,581177735,569920802,981786970,598460733,377572566,264417139},{706335400,596316849,447775470,746839035,920210481,622221732,540355931,451875151,359873792,789740009,210319930}},{{2640,20880,191520,1975680,22498560,279417600,757446141,221985738,886752445,63394417,307555505},{17040,147840,1491840,16934400,211680000,877520894,66210774,66317679,451042652,551342463,407701052},{141120,1330560,14515200,177811200,398519294,28564445,939924956,818103343,801908092,190783580,969578907},{1395072,14224896,166199040,174985214,189529057,66547228,973162637,194827075,449888597,212424334,317413981},{15724800,172972800,159018494,908680163,292152891,186919681,105698228,622625275,381187180,452937560,386152310},{196473600,330090494,914058210,697347644,571124681,411032220,40149965,3453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};
mint solve(int n, int a1, int a2) {
if (n <= 20) return TLE(n, a1, a2);
if (a1 == a2) {
mint res = n;
repi(i, 1, n) res *= i;
return res;
}
if (a1 > a2) swap(a1, a2);
int n0 = a1 - 1, n1 = a2 - a1 - 1, n2 = n - a2 - 1;
// 計算する初項の数
int N0 = 14, N1 = 14, N2 = 11;
//vvvm seq012(N0, vvm(N1, vm(N2))); // 埋め込める
//rep(i0, N0) rep(i1, N1) rep(i2, N2) {
// int a1 = i0 + 1;
// int a2 = a1 + i1 + 1;
// int n = a2 + i2 + 1;
// mute_dump = 1;
// seq012[i0][i1][i2] = TLE(n, a1, a2);
// mute_dump = 0;
//}
//dump_math(seq012);
vvm seq01(N0, vm(N1));
rep(i0, N0) rep(i1, N1) {
dump("i0:", i0, "i1:", i1);
if (!p_recursive_edited(n, seq012[i0][i1], 3, 3)) { // 除算回避できる
exit(-1);
}
seq01[i0][i1] = seq012[i0][i1][n2];
}
dumpel(seq01);
vm seq0(N0);
rep(i0, N0) {
dump("i0:", i0);
if (!p_recursive(n, seq01[i0], 3, 4)) {
exit(-1);
}
seq0[i0] = seq01[i0][n1];
}
dumpel(seq0);
if (!p_recursive(n, seq0, 3, 4)) {
dump("failed...");
exit(-1);
}
return seq0[n0];
}
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
// bug_find();
// zikken2();
int n, a1, a2;
cin >> n >> a1 >> a2;
dump(n, a1, a2); dump("====");
// dump(naive(n, a1, a2)); dump("====");
EXIT(solve(n, a1, a2));
}