結果
問題 | No.1080 Strange Squared Score Sum |
ユーザー | heno239 |
提出日時 | 2023-12-13 05:40:41 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 2,989 ms / 5,000 ms |
コード長 | 16,078 bytes |
コンパイル時間 | 3,390 ms |
コンパイル使用メモリ | 190,300 KB |
実行使用メモリ | 33,852 KB |
最終ジャッジ日時 | 2024-09-27 05:11:10 |
合計ジャッジ時間 | 36,482 ms |
ジャッジサーバーID (参考情報) |
judge3 / judge2 |
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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 | 18 ms
11,776 KB |
testcase_01 | AC | 17 ms
11,776 KB |
testcase_02 | AC | 1,444 ms
23,048 KB |
testcase_03 | AC | 2,889 ms
33,484 KB |
testcase_04 | AC | 698 ms
17,100 KB |
testcase_05 | AC | 697 ms
17,200 KB |
testcase_06 | AC | 179 ms
12,904 KB |
testcase_07 | AC | 343 ms
14,404 KB |
testcase_08 | AC | 1,442 ms
22,732 KB |
testcase_09 | AC | 1,399 ms
22,500 KB |
testcase_10 | AC | 171 ms
13,036 KB |
testcase_11 | AC | 2,916 ms
33,468 KB |
testcase_12 | AC | 1,399 ms
22,508 KB |
testcase_13 | AC | 2,989 ms
33,512 KB |
testcase_14 | AC | 1,419 ms
22,548 KB |
testcase_15 | AC | 19 ms
11,848 KB |
testcase_16 | AC | 2,955 ms
33,852 KB |
testcase_17 | AC | 1,421 ms
22,996 KB |
testcase_18 | AC | 1,416 ms
22,868 KB |
testcase_19 | AC | 1,441 ms
22,996 KB |
testcase_20 | AC | 2,957 ms
33,456 KB |
testcase_21 | AC | 2,986 ms
33,452 KB |
ソースコード
#pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include<iostream> #include<string> #include<cstdio> #include<vector> #include<cmath> #include<algorithm> #include<functional> #include<iomanip> #include<queue> #include<ciso646> #include<random> #include<map> #include<set> #include<bitset> #include<stack> #include<unordered_map> #include<unordered_set> #include<utility> #include<cassert> #include<complex> #include<numeric> #include<array> #include<chrono> using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; //ll mod = 1; //constexpr ll mod = 998244353; constexpr ll mod = 1000000009; const int mod17 = 1000000007; const ll INF = (ll)mod17 * mod17; typedef pair<int, int>P; #define rep(i,n) for(int i=0;i<n;i++) #define per(i,n) for(int i=n-1;i>=0;i--) #define Rep(i,sta,n) for(int i=sta;i<n;i++) #define rep1(i,n) for(int i=1;i<=n;i++) #define per1(i,n) for(int i=n;i>=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair<ll, ll> LP; using ld = double; typedef pair<ld, ld> LDP; const ld eps = 1e-10; const ld pi = acosl(-1.0); template<typename T> void chmin(T& a, T b) { a = min(a, b); } template<typename T> void chmax(T& a, T b) { a = max(a, b); } template<typename T> vector<T> vmerge(vector<T>& a, vector<T>& b) { vector<T> res; int ida = 0, idb = 0; while (ida < a.size() || idb < b.size()) { if (idb == b.size()) { res.push_back(a[ida]); ida++; } else if (ida == a.size()) { res.push_back(b[idb]); idb++; } else { if (a[ida] < b[idb]) { res.push_back(a[ida]); ida++; } else { res.push_back(b[idb]); idb++; } } } return res; } template<typename T> void cinarray(vector<T>& v) { rep(i, v.size())cin >> v[i]; } template<typename T> void coutarray(vector<T>& v) { rep(i, v.size()) { if (i > 0)cout << " "; cout << v[i]; } cout << "\n"; } ll mod_pow(ll x, ll n, ll m = mod) { if (n < 0) { ll res = mod_pow(x, -n, m); return mod_pow(res, m - 2, m); } if (abs(x) >= m)x %= m; if (x < 0)x += m; //if (x == 0)return 0; ll res = 1; while (n) { if (n & 1)res = res * x % m; x = x * x % m; n >>= 1; } return res; } //mod should be <2^31 struct modint { int n; modint() :n(0) { ; } modint(ll m) { if (m < 0 || mod <= m) { m %= mod; if (m < 0)m += mod; } n = m; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } bool operator<(modint a, modint b) { return a.n < b.n; } modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; } modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; } modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, ll n) { if (n == 0)return modint(1); modint res = (a * a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } modint operator/=(modint& a, modint b) { a = a / b; return a; } const int max_n = 1 << 20; modint fact[max_n], factinv[max_n]; void init_f() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } modint combP(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[a - b]; } ll gcd(ll a, ll b) { a = abs(a); b = abs(b); if (a < b)swap(a, b); while (b) { ll r = a % b; a = b; b = r; } return a; } template<typename T> void addv(vector<T>& v, int loc, T val) { if (loc >= v.size())v.resize(loc + 1, 0); v[loc] += val; } /*const int mn = 2000005; bool isp[mn]; vector<int> ps; void init() { fill(isp + 2, isp + mn, true); for (int i = 2; i < mn; i++) { if (!isp[i])continue; ps.push_back(i); for (int j = 2 * i; j < mn; j += i) { isp[j] = false; } } }*/ //[,val) template<typename T> auto prev_itr(set<T>& st, T val) { auto res = st.lower_bound(val); if (res == st.begin())return st.end(); res--; return res; } //[val,) template<typename T> auto next_itr(set<T>& st, T val) { auto res = st.lower_bound(val); return res; } using mP = pair<modint, modint>; mP operator+(mP a, mP b) { return { a.first + b.first,a.second + b.second }; } mP operator+=(mP& a, mP b) { a = a + b; return a; } mP operator-(mP a, mP b) { return { a.first - b.first,a.second - b.second }; } mP operator-=(mP& a, mP b) { a = a - b; return a; } LP operator+(LP a, LP b) { return { a.first + b.first,a.second + b.second }; } LP operator+=(LP& a, LP b) { a = a + b; return a; } LP operator-(LP a, LP b) { return { a.first - b.first,a.second - b.second }; } LP operator-=(LP& a, LP b) { a = a - b; return a; } mt19937 mt(time(0)); const string drul = "DRUL"; string senw = "SENW"; //DRUL,or SENW //int dx[4] = { 1,0,-1,0 }; //int dy[4] = { 0,1,0,-1 }; //------------------------------------ modint r2 = 291087696; modint ri = 430477711; void expr() { for (ll c = 1; c < mod; c++) { if (c * c % mod == mod - 1) { cout << "! -1 " << c << "\n"; } if (c * c % mod == 2) { cout << "! 2 " << c << "\n"; } } } int bsf(int x) { int res = 0; while (!(x & 1)) { res++; x >>= 1; } return res; } int ceil_pow2(int n) { int x = 0; while ((1 << x) < n) x++; return x; } int get_premitive_root(const ll& p) { int primitive_root = 0; if (!primitive_root) { primitive_root = [&]() { set<int> fac; int v = p - 1; for (ll i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i; if (v > 1) fac.insert(v); for (int g = 1; g < p; g++) { bool ok = true; for (auto i : fac) if (mod_pow(g, (p - 1) / i, p) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } const array<ll, 3> ms = { 469762049,167772161,595591169 }; const array<ll, 3> proots = { get_premitive_root(469762049),get_premitive_root(167772161),get_premitive_root(595591169) }; using poly = vector<ll>; using polys = array<poly, 3>; void butterfly(polys& a) { int n = int(a[0].size()); array<ll, 3> gs = proots; int h = ceil_pow2(n); static bool first = true; static ll sum_e[3][30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i] if (first) { first = false; ll es[3][30], ies[3][30]; // es[i]^(2^(2+i)) == 1 int cnt2[3]; rep(i, 3)cnt2[i] = bsf(ms[i] - 1); ll e[3]; rep(i, 3)e[i] = mod_pow(gs[i], (ms[i] - 1) >> cnt2[i], ms[i]); ll ie[3]; rep(i, 3)ie[i] = mod_pow(e[i], ms[i] - 2, ms[i]); rep(j, 3) { for (int i = cnt2[j]; i >= 2; i--) { // e^(2^i) == 1 es[j][i - 2] = e[j]; ies[j][i - 2] = ie[j]; e[j] *= e[j]; e[j] %= ms[j]; ie[j] *= ie[j]; ie[j] %= ms[j]; } } rep(j, 3) { ll now = 1; for (int i = 0; i < cnt2[j] - 2; i++) { sum_e[j][i] = es[j][i] * now % ms[j]; now *= ies[j][i]; now %= ms[j]; } } } for (int ph = 1; ph <= h; ph++) { int w = 1 << (ph - 1), p = 1 << (h - ph); ll now[3] = { 1,1,1 }; for (int s = 0; s < w; s++) { int offset = s << (h - ph + 1); for (int i = 0; i < p; i++) { rep(j, 3) { auto l = a[j][i + offset]; auto r = a[j][i + offset + p] * now[j] % ms[j]; a[j][i + offset] = l + r; if (a[j][i + offset] >= ms[j])a[j][i + offset] -= ms[j]; a[j][i + offset + p] = l - r; if (a[j][i + offset + p] < 0)a[j][i + offset + p] += ms[j]; } } rep(j, 3) { now[j] *= sum_e[j][bsf(~(unsigned int)(s))]; now[j] %= ms[j]; } } } } void butterfly_inv(polys& a) { int n = int(a[0].size()); array<ll, 3> gs = proots; int h = ceil_pow2(n); static bool first = true; static ll sum_ie[3][30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i] if (first) { first = false; ll es[3][30], ies[3][30]; // es[i]^(2^(2+i)) == 1 int cnt2[3]; rep(i, 3)cnt2[i] = bsf(ms[i] - 1); ll e[3]; rep(i, 3)e[i] = mod_pow(gs[i], (ms[i] - 1) >> cnt2[i], ms[i]); ll ie[3]; rep(i, 3)ie[i] = mod_pow(e[i], ms[i] - 2, ms[i]); rep(j, 3) { for (int i = cnt2[j]; i >= 2; i--) { // e^(2^i) == 1 es[j][i - 2] = e[j]; ies[j][i - 2] = ie[j]; e[j] *= e[j]; e[j] %= ms[j]; ie[j] *= ie[j]; ie[j] %= ms[j]; } } rep(j, 3) { ll now = 1; for (int i = 0; i < cnt2[j] - 2; i++) { sum_ie[j][i] = ies[j][i] * now % ms[j]; now *= es[j][i]; now %= ms[j]; } } } for (int ph = h; ph >= 1; ph--) { int w = 1 << (ph - 1), p = 1 << (h - ph); ll inow[3] = { 1,1,1 }; for (int s = 0; s < w; s++) { int offset = s << (h - ph + 1); for (int i = 0; i < p; i++) { rep(j, 3) { auto l = a[j][i + offset]; auto r = a[j][i + offset + p]; a[j][i + offset] = l + r; if (a[j][i + offset] >= ms[j])a[j][i + offset] -= ms[j]; a[j][i + offset + p] = (ms[j] + l - r) * inow[j] % ms[j]; } } rep(j, 3) { inow[j] *= sum_ie[j][bsf(~(unsigned int)(s))]; inow[j] %= ms[j]; } } } } constexpr ll m0 = 469762049; constexpr ll m1 = 167772161; constexpr ll m2 = 595591169; const ll inv01 = mod_pow(m0, m1 - 2, m1); const ll inv012 = mod_pow(m0 * m1, m2 - 2, m2); ll calc(ll& a, ll& b, ll& c, const ll& p) { ll res = 0; ll x1 = a; ll x2 = (b - x1) * inv01; x2 %= m1; if (x2 < 0)x2 += m1; ll x3 = (c - x1 - x2 * m0) % m2 * inv012; x3 %= m2; if (x3 < 0)x3 += m2; res = x1 + x2 * m0 % p + x3 * m0 % p * m1; return res % p; } using poly2 = vector<modint>; vector<modint> multiply(poly2 _g, poly2 _h, const ll& p=mod) { poly g(_g.size()), h(_h.size()); rep(i, g.size())g[i] = _g[i]; rep(i, h.size())h[i] = _h[i]; int n = g.size(); int m = h.size(); if (n == 0 || m == 0)return {}; if (min(g.size(), h.size()) < 60) { vector<modint> res(g.size() + h.size() - 1); rep(i, g.size())rep(j, h.size()) { res[i + j] += g[i] * h[j]; } return res; } int z = 1 << ceil_pow2(n + m - 1); g.resize(z); h.resize(z); polys gs, hs; rep(j, 3) { gs[j].resize(z); hs[j].resize(z); rep(i, z) { gs[j][i] = g[i] % ms[j]; hs[j][i] = h[i] % ms[j]; } } butterfly(gs); butterfly(hs); rep(j, 3)rep(i, z) { (gs[j][i] *= hs[j][i]) %= ms[j]; } butterfly_inv(gs); rep(j, 3) { gs[j].resize(n + m - 1); ll iz = mod_pow(z, ms[j] - 2, ms[j]); rep(i, n + m - 1) { (gs[j][i] *= iz) %= ms[j]; } } vector<modint> res(n + m - 1); rep(i, n + m - 1) { res[i] = calc(gs[0][i], gs[1][i], gs[2][i], p); } return res; } struct FormalPowerSeries :vector<modint> { using vector<modint>::vector; using fps = FormalPowerSeries; void shrink() { while (this->size() && this->back() == (modint)0)this->pop_back(); } fps operator+(const fps& r)const { return fps(*this) += r; } fps operator+(const modint& v)const { return fps(*this) += v; } fps operator-(const fps& r)const { return fps(*this) -= r; } fps operator-(const modint& v)const { return fps(*this) -= v; } fps operator*(const fps& r)const { return fps(*this) *= r; } fps operator*(const modint& v)const { return fps(*this) *= v; } fps& operator+=(const fps& r) { if (r.size() > this->size())this->resize(r.size()); rep(i, r.size())(*this)[i] += r[i]; shrink(); return *this; } fps& operator+=(const modint& v) { if (this->empty())this->resize(1); (*this)[0] += v; shrink(); return *this; } fps& operator-=(const fps& r) { if (r.size() > this->size())this->resize(r.size()); rep(i, r.size())(*this)[i] -= r[i]; shrink(); return *this; } fps& operator-=(const modint& v) { if (this->empty())this->resize(1); (*this)[0] -= v; shrink(); return *this; } fps& operator*=(const fps& r) { if (this->empty() || r.empty())this->clear(); else { poly2 ret = multiply(*this, r); *this = fps(all(ret)); } shrink(); return *this; } fps& operator*=(const modint& v) { for (auto& x : (*this))x *= v; shrink(); return *this; } fps operator-()const { fps ret = *this; for (auto& v : ret)v = -v; return ret; } modint sub(modint x) { modint t = 1; modint res = 0; rep(i, (*this).size()) { res += t * (*this)[i]; t *= x; } return res; } fps pre(int sz)const { fps ret(this->begin(), this->begin() + min((int)this->size(), sz)); ret.shrink(); return ret; } fps integral() const { const int n = (int)this->size(); fps ret(n + 1); ret[0] = 0; for (int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / (modint)(i + 1); return ret; } fps inv(int deg = -1)const { const int n = this->size(); if (deg == -1)deg = n; fps ret({ (modint)1 / (*this)[0] }); for (int i = 1; i < deg; i <<= 1) { ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1); } ret = ret.pre(deg); ret.shrink(); return ret; } fps diff() const { const int n = (int)this->size(); fps ret(max(0, n - 1)); for (int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * (modint)i; return ret; } // F(0) must be 1 fps log(int deg = -1) const { assert((*this)[0] == 1); const int n = (int)this->size(); if (deg == -1) deg = n; return (this->diff() * this->inv(deg)).pre(deg - 1).integral(); } // F(0) must be 0 fps exp(int deg = -1)const { assert((*this)[0] == 0); const int n = (int)this->size(); if (deg == -1)deg = n; fps ret = { 1 }; for (int i = 1; i < deg; i <<= 1) { ret = (ret * (pre(i << 1) + 1 - ret.log(i << 1))).pre(i << 1); } //cout << "!!!! " << ret.size() << "\n"; return ret.pre(deg); } fps div(fps g) { assert(g.size() && g.back() != (modint)0); fps f = *this; if (f.size() < g.size())return {}; int dif = f.size() - g.size(); reverse(all(f)); reverse(all(g)); g = g.inv(dif + 1); fps fg = f * g; fps ret(dif + 1); rep(i, fg.size()) { int id = i - dif; if (-dif <= id && id <= 0) { ret[-id] = fg[i]; } } return ret; } fps divr(fps g) { fps ret = (*this) - g * (*this).div(g); ret.shrink(); return ret; } }; using fps = FormalPowerSeries; void solve() { int n; cin >> n; auto calc = [&](modint r,modint s) { fps f(n + 1); rep1(i, n) { f[i] = (modint)(i + 1) * (modint)(i + 1) * r; } f = f.exp(n+1); rep(i, f.size())f[i] *= s; return f; /*vector<modint> res(n + 1); res[0] = s; for (int i = 1; i <= n; i++) { modint c = (modint)(i + 1) * (modint)(i + 1); for (int j = n-i; j >= 0; j--) { modint pro = res[j]; int t = 0; for (int k = j + i; k <= n; k += i) { pro *= r * c; t++; res[k] += pro * factinv[t]; } } } return res;*/ }; modint t1 = ri; modint s1 = (modint)1 / r2 - (modint)1 / r2 * ri; modint t2 = -ri; modint s2 = (modint)1 / r2 + (modint)1 / r2 * ri; auto v1 = calc(t1,s1); auto v2 = calc(t2,s2); vector<modint> ans(n + 1); modint cc = (modint)1 / r2; rep(i, n + 1) { ans[i] = v1[i] + v2[i]; ans[i] *= cc; ans[i] *= fact[n]; } rep1(i, n)cout << ans[i] << "\n"; } signed main() { ios::sync_with_stdio(false); cin.tie(0); //cout << fixed<<setprecision(10); init_f(); //init(); //while(true) //expr(); //int t; cin >> t; rep(i, t) solve(); return 0; }