結果
| 問題 | No.1080 Strange Squared Score Sum |
| ユーザー |
👑  hos.lyric
|
| 提出日時 | 2020-06-12 22:24:09 |
| 言語 | D (dmd 2.109.1) |
| 結果 |
TLE
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 13,225 bytes |
| コンパイル時間 | 1,680 ms |
| コンパイル使用メモリ | 162,072 KB |
| 実行使用メモリ | 54,700 KB |
| 最終ジャッジ日時 | 2024-06-22 07:19:54 |
| 合計ジャッジ時間 | 55,224 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 19 TLE * 1 |
ソースコード
import std.conv, std.functional, std.range, std.stdio, std.string;import std.algorithm, std.array, std.bigint, std.bitmanip, std.complex, std.container, std.math, std.mathspecial, std.numeric, std.regex, std.typecons;import core.bitop;class EOFException : Throwable { this() { super("EOF"); } }string[] tokens;string readToken() { for (; tokens.empty; ) { if (stdin.eof) { throw new EOFException; } tokens = readln.split; } auto token = tokens.front; tokens.popFront; return token; }int readInt() { return readToken.to!int; }long readLong() { return readToken.to!long; }real readReal() { return readToken.to!real; }bool chmin(T)(ref T t, in T f) { if (t > f) { t = f; return true; } else { return false; } }bool chmax(T)(ref T t, in T f) { if (t < f) { t = f; return true; } else { return false; } }int binarySearch(alias pred, T)(in T[] as) { int lo = -1, hi = cast(int)(as.length); for (; lo + 1 < hi; ) { const mid = (lo + hi) >> 1;(unaryFun!pred(as[mid]) ? hi : lo) = mid; } return hi; }int lowerBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a >= val)); }int upperBound(T)(in T[] as, T val) { return as.binarySearch!(a => (a > val)); }struct ModInt(int M_) {import std.conv : to;alias M = M_;int x;this(ModInt a) { x = a.x; }this(long a) { x = cast(int)(a % M); if (x < 0) x += M; }ref ModInt opAssign(long a) { return (this = ModInt(a)); }ref ModInt opOpAssign(string op)(ModInt a) {static if (op == "+") { x += a.x; if (x >= M) x -= M; }else static if (op == "-") { x -= a.x; if (x < 0) x += M; }else static if (op == "*") { x = cast(int)((cast(long)(x) * a.x) % M); }else static if (op == "/") { this *= a.inv(); }else static assert(false);return this;}ref ModInt opOpAssign(string op)(long a) {static if (op == "^^") {if (a < 0) return (this = inv()^^(-a));ModInt t2 = this, te = ModInt(1);for (long e = a; e > 0; e >>= 1) {if (e & 1) te *= t2;t2 *= t2;}x = cast(int)(te.x);return this;} else return mixin("this " ~ op ~ "= ModInt(a)");}ModInt inv() const {int a = x, b = M, y = 1, z = 0, t;for (; ; ) {t = a / b; a -= t * b;if (a == 0) {assert(b == 1 || b == -1);return ModInt(b * z);}y -= t * z;t = b / a; b -= t * a;if (b == 0) {assert(a == 1 || a == -1);return ModInt(a * y);}z -= t * y;}}ModInt opUnary(string op: "-")() const { return ModInt(-x); }ModInt opBinary(string op, T)(T a) const {return mixin("ModInt(this) " ~ op ~ "= a");}ModInt opBinaryRight(string op)(long a) const {return mixin("ModInt(a) " ~ op ~ "= this");}bool opCast(T: bool)() const { return (x != 0); }string toString() const { return x.to!string; }}enum MO = 10^^9 + 9;alias Mint = ModInt!MO;enum Mint I = 569522298;// a^-1 (mod m)long modInv(long a, long m)in {assert(m > 0, "modInv: m > 0 must hold");}do {long b = m, x = 1, y = 0, t;for (; ; ) {t = a / b; a -= t * b;if (a == 0) {assert(b == 1 || b == -1, "modInv: gcd(a, m) != 1");if (b == -1) y = -y;return (y < 0) ? (y + m) : y;}x -= t * y;t = b / a; b -= t * a;if (b == 0) {assert(a == 1 || a == -1, "modInv: gcd(a, m) != 1");if (a == -1) x = -x;return (x < 0) ? (x + m) : x;}y -= t * x;}}// M: prime, G: primitive rootclass Fft(int M_, int G, int K) {import std.algorithm : reverse;import std.traits : isIntegral;alias M = M_;// 1, 1/4, 1/8, 3/8, 1/16, 5/16, 3/16, 7/16, ...int[] gs;this() {static assert(2 <= K && K <= 30, "Fft: 2 <= K <= 30 must hold");static assert(!((M - 1) & ((1 << K) - 1)), "Fft: 2^K | M - 1 must hold");gs = new int[1 << (K - 1)];gs[0] = 1;long g2 = G, gg = 1;for (int e = (M - 1) >> K; e; e >>= 1) {if (e & 1) gg = (gg * g2) % M;g2 = (g2 * g2) % M;}gs[1 << (K - 2)] = cast(int)(gg);for (int l = 1 << (K - 2); l >= 2; l >>= 1) {gs[l >> 1] = cast(int)((cast(long)(gs[l]) * gs[l]) % M);}assert((cast(long)(gs[1]) * gs[1]) % M == M - 1,"Fft: g^(2^(K-1)) == -1 (mod M) must hold");for (int l = 2; l <= 1 << (K - 2); l <<= 1) {foreach (i; 1 .. l) {gs[l + i] = cast(int)((cast(long)(gs[l]) * gs[i]) % M);}}}void fft(int[] xs) const {const n = cast(int)(xs.length);assert(!(n & (n - 1)), "Fft.fft: |xs| must be a power of two");assert(n <= 1 << K, "Fft.fft: |xs| <= 2^K must hold");for (int l = n; l >>= 1; ) {foreach (i; 0 .. (n >> 1) / l) {const(long) g = gs[i];foreach (j; (i << 1) * l .. (i << 1 | 1) * l) {const t = cast(int)((g * xs[j + l]) % M);if ((xs[j + l] = xs[j] - t) < 0) xs[j + l] += M;if ((xs[j] += t) >= M) xs[j] -= M;}}}}void invFft(int[] xs) const {const n = cast(int)(xs.length);assert(!(n & (n - 1)), "Fft.invFft: |xs| must be a power of two");assert(n <= 1 << K, "Fft.invFft: |xs| <= 2^K must hold");for (int l = 1; l < n; l <<= 1) reverse(xs[l .. l << 1]);for (int l = 1; l < n; l <<= 1) {foreach (i; 0 .. (n >> 1) / l) {const(long) g = gs[i];foreach (j; (i << 1) * l .. (i << 1 | 1) * l) {int t = cast(int)((g * (xs[j] - xs[j + l])) % M);if (t < 0) t += M;if ((xs[j] += xs[j + l]) >= M) xs[j] -= M;xs[j + l] = t;}}}}T[] convolute(T)(inout(T)[] as, inout(T)[] bs) const if (isIntegral!T) {const na = cast(int)(as.length), nb = cast(int)(bs.length);int n, invN = 1;for (n = 1; n < na + nb - 1; n <<= 1) {invN = ((invN & 1) ? (invN + M) : invN) >> 1;}auto xs = new int[n], ys = new int[n];foreach (i; 0 .. na) if ((xs[i] = cast(int)(as[i] % M)) < 0) xs[i] += M;foreach (i; 0 .. nb) if ((ys[i] = cast(int)(bs[i] % M)) < 0) ys[i] += M;fft(xs);fft(ys);foreach (i; 0 .. n) {xs[i] = cast(int)((((cast(long)(xs[i]) * ys[i]) % M) * invN) % M);}invFft(xs);auto cs = new T[na + nb - 1];foreach (i; 0 .. na + nb - 1) cs[i] = cast(T)(xs[i]);return cs;}ModInt!M[] convolute(inout(ModInt!M)[] as, inout(ModInt!M)[] bs) const {const na = cast(int)(as.length), nb = cast(int)(bs.length);int n, invN = 1;for (n = 1; n < na + nb - 1; n <<= 1) {invN = ((invN & 1) ? (invN + M) : invN) >> 1;}auto xs = new int[n], ys = new int[n];foreach (i; 0 .. na) xs[i] = as[i].x;foreach (i; 0 .. nb) ys[i] = bs[i].x;fft(xs);fft(ys);foreach (i; 0 .. n) {xs[i] = cast(int)((((cast(long)(xs[i]) * ys[i]) % M) * invN) % M);}invFft(xs);auto cs = new ModInt!M[na + nb - 1];foreach (i; 0 .. na + nb - 1) cs[i].x = xs[i];return cs;}int[] convolute(int M1)(inout(ModInt!M1)[] as, inout(ModInt!M1)[] bs) constif (M != M1) {const na = cast(int)(as.length), nb = cast(int)(bs.length);int n, invN = 1;for (n = 1; n < na + nb - 1; n <<= 1) {invN = ((invN & 1) ? (invN + M) : invN) >> 1;}auto xs = new int[n], ys = new int[n];foreach (i; 0 .. na) xs[i] = as[i].x;foreach (i; 0 .. nb) ys[i] = bs[i].x;fft(xs);fft(ys);foreach (i; 0 .. n) {xs[i] = cast(int)((((cast(long)(xs[i]) * ys[i]) % M) * invN) % M);}invFft(xs);return xs[0 .. na + nb - 1];}}enum FFT_K = 20;alias Fft3_0 = Fft!(1045430273, 3, FFT_K); // 2^20 997 + 1alias Fft3_1 = Fft!(1051721729, 6, FFT_K); // 2^20 1003 + 1alias Fft3_2 = Fft!(1053818881, 7, FFT_K); // 2^20 1005 + 1enum long FFT_INV01 = modInv(Fft3_0.M, Fft3_1.M);enum long FFT_INV012 = modInv(cast(long)(Fft3_0.M) * Fft3_1.M, Fft3_2.M);Fft3_0 FFT3_0;Fft3_1 FFT3_1;Fft3_2 FFT3_2;void initFft3() {FFT3_0 = new Fft3_0;FFT3_1 = new Fft3_1;FFT3_2 = new Fft3_2;}ModInt!M[] convolute(int M)(inout(ModInt!M)[] as, inout(ModInt!M)[] bs) {const cs0 = FFT3_0.convolute(as, bs);const cs1 = FFT3_1.convolute(as, bs);const cs2 = FFT3_2.convolute(as, bs);auto cs = new ModInt!M[cs0.length];foreach (i; 0 .. cs0.length) {long d0 = cs0[i] % Fft3_0.M;long d1 = (FFT_INV01 * (cs1[i] - d0)) % Fft3_1.M;if (d1 < 0) d1 += Fft3_1.M;long d2 =(FFT_INV012 * ((cs2[i] - d0 - Fft3_0.M * d1) % Fft3_2.M)) % Fft3_2.M;if (d2 < 0) d2 += Fft3_2.M;cs[i] =(d0 + Fft3_0.M * d1 + ((cast(long)(Fft3_0.M) * Fft3_1.M) % M) * d2) % M;}return cs;}struct Poly {Mint[] x;this(Poly f) {x = f.x.dup;}this(const(Poly) f) {x = f.x.dup;}this(int n) {x = new Mint[n];}this(const(Mint)[] x) {this.x = x.dup;}this(const(long)[] x) {this.x.length = x.length;foreach (i; 0 .. x.length) this.x[i] = Mint(x[i]);}int size() const {return cast(int)(x.length);}Poly take(int n) const {return Poly(x[0 .. min(max(n, 1), $)]);}ref Poly opAssign(const(Mint)[] x) {this.x = x.dup;return this;}ref Poly opAssign(const(long)[] x) {this.x.length = x.length;foreach (i; 0 .. x.length) this.x[i] = Mint(x[i]);return this;}Mint opIndex(int i) const {return x[i];}ref Mint opIndex(int i) {return x[i];}ref Poly opOpAssign(string op)(const(Poly) f) {static if (op == "+") {if (size() < f.size()) x.length = f.size();foreach (i; 0 .. f.size()) this[i] += f[i];return this;} else static if (op == "-") {if (size() < f.size()) x.length = f.size();foreach (i; 0 .. f.size()) this[i] -= f[i];return this;} else static if (op == "*") {// TODO: FFT/*Poly g = Poly(size() + f.size() - 1);foreach (i; 0 .. size()) foreach (j; 0 .. f.size()) {g[i + j] += this[i] * f[j];}this = g;return this;*/return this = Poly(convolute!MO(x, f.x));} else {static assert(false);}}ref Poly opOpAssign(string op)(Mint a) if (op == "*") {foreach (i; 0 .. size()) this[i] *= a;return this;}Poly opBinary(string op, T)(T a) const {return mixin("Poly(this) " ~ op ~ "= a");// Poly f = Poly(this);// mixin("f " ~ op ~ "= a;");// return f;}Poly opBinaryRight(string op)(Mint a) const if (op == "*") {return this * a;}Poly opUnary(string op)() const if (op == "-") {return this * Mint(-1);}Poly square(int n) const {// TODO: FFT/*Poly f = Poly(n);foreach (i; 0 .. min(size(), (n + 1) / 2)) {f[i + i] += this[i] * this[i];foreach (j; i + 1 .. min(size(), n - i)) {f[i + j] += Mint(2) * this[i] * this[j];}}return f;*/return Poly(convolute!MO(x, x));}Poly inv(int n) const {// TODO: fftassert(this[0].x != 0);Poly f = Poly(n);f[0] = this[0].inv();foreach (i; 1 .. n) {foreach (j; 1 .. min(size(), i + 1)) {f[i] -= this[j] * f[i - j];}f[i] *= f[0];}return f;}Poly differential() const {Poly f = Poly(max(size() - 1, 1));foreach (i; 1 .. size()) f[i - 1] = Mint(i) * this[i];return f;}Poly integral() const {Poly f = Poly(size() + 1);foreach (i; 0 .. size()) f[i + 1] = Mint(i + 1).inv() * this[i];return f;}Poly exp(int n) const {assert(this[0].x == 0);const d = differential();Poly f = [1], g = [1];for (int m = 1; m < n; m <<= 1) {g = g + g - (f * g.square(m)).take(m);Poly h = d.take(m - 1);h += (g * (f.differential() - f * h)).take(2 * m - 1);f += (f * (take(2 * m) - h.integral())).take(2 * m);}return f.take(n);}}enum Poly1 = Poly([1]);enum PolyQ = Poly([0, 1]);void main() {initFft3;debug {// N = 3auto sums = new Mint[][](3 + 1, 9 + 1);sums[0][0] += 6 * 1^^2;foreach (a; 1 .. 3 + 1) {sums[1][a] += 6 * (a + 1)^^2;}// foreach (a; 1 .. 3 + 1) foreach (b; a .. 3 + 1) {foreach (a; 1 .. 3 + 1) foreach (b; 1 .. 3 + 1) {sums[2][a + b] += 3 * ((a + 1) * (b + 1))^^2;}// foreach (a; 1 .. 3 + 1) foreach (b; a .. 3 + 1) foreach (c; b .. 3 + 1) {foreach (a; 1 .. 3 + 1) foreach (b; 1 .. 3 + 1) foreach (c; 1 .. 3 + 1) {sums[3][a + b + c] += 1 * ((a + 1) * (b + 1) * (c + 1))^^2;}foreach (m; 0 .. 3 + 1) {writeln(sums[m]);}foreach (k; 0 .. 9 + 1) {writeln(sums[0][k] + sums[1][k] - sums[2][k] - sums[3][k]);}}try {for (; ; ) {const N = readInt();Mint fac = 1;foreach (i; 1 .. N + 1) {fac *= i;}auto f = Poly(N + 1);foreach (i; 1 .. N + 1) {f[i] = 1L * (i + 1) * (i + 1);}auto g0 = (f * I).exp(N + 1);auto g1 = (f * -I).exp(N + 1);auto re = (g0 + g1) * Mint(2).inv;auto im = (g0 - g1) * Mint(2 * I).inv;auto ans = (re + im) * fac;foreach (i; 1 .. N + 1) {writeln(ans[i]);}}} catch (EOFException e) {}}