結果
問題 | No.1321 塗るめた |
ユーザー |
👑 |
提出日時 | 2020-12-18 00:31:01 |
言語 | D (dmd 2.109.1) |
結果 |
AC
|
実行時間 | 1,213 ms / 2,000 ms |
コード長 | 12,951 bytes |
コンパイル時間 | 1,600 ms |
コンパイル使用メモリ | 158,700 KB |
実行使用メモリ | 31,440 KB |
最終ジャッジ日時 | 2024-06-22 10:22:47 |
合計ジャッジ時間 | 24,828 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge1 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 45 |
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 = 998244353;alias Mint = ModInt!MO;enum LIM = 2 * 10^^5;Mint[] inv, fac, invFac;void prepare() {inv = new Mint[LIM];fac = new Mint[LIM];invFac = new Mint[LIM];inv[1] = 1;foreach (i; 2 .. LIM) {inv[i] = -(Mint.M / i) * inv[cast(size_t)(Mint.M % i)];}fac[0] = invFac[0] = 1;foreach (i; 1 .. LIM) {fac[i] = fac[i - 1] * i;invFac[i] = invFac[i - 1] * inv[i];}}Mint binom(long n, long k) {if (0 <= k && k <= n) {assert(n < LIM);return fac[cast(size_t)(n)] * invFac[cast(size_t)(k)] * invFac[cast(size_t)(n - k)];} else {return Mint(0);}}// 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];}ModInt!M[] square(inout(ModInt!M)[] as) const {const na = cast(int)(as.length);int n, invN = 1;for (n = 1; n < na + na - 1; n <<= 1) {invN = ((invN & 1) ? (invN + M) : invN) >> 1;}auto xs = new int[n];foreach (i; 0 .. na) xs[i] = as[i].x;fft(xs);foreach (i; 0 .. n) {xs[i] = cast(int)((((cast(long)(xs[i]) * xs[i]) % M) * invN) % M);}invFft(xs);auto cs = new ModInt!M[na + na - 1];foreach (i; 0 .. na + na - 1) cs[i].x = xs[i];return cs;}}alias Fft0 = Fft!(998244353, 3, 20);Fft0 FFT;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;*/x = FFT.convolute(x, f.x);return this;} 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;*/Poly f;f.x = x.dup;f.x = FFT.square(f.x);return f.take(n);}Poly inv(int n) const {// TODO: fft/*assert(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 f = Poly([this[0].inv()]);for (int m = 1; m < n; m <<= 1) {f = (f + f - f.square(m << 1) * this.take(m << 1)).take(m << 1);}return f.take(n);}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);}Poly log(int n) const {assert(this[0].x == 1);return (differential() * inv(n)).take(n).integral().take(n);}}enum Poly1 = Poly([1]);enum PolyQ = Poly([0, 1]);void main() {prepare;FFT = new Fft0;try {for (; ; ) {const N = readInt();const M = readInt();const K = readInt();// \sum_{a=K}^\infty S(a, K) x^a/a! = (1/K!) (e^x - 1)^Kauto fs = new Mint[N - K + 1];fs[0 .. N - K + 1] = invFac[1 .. N - K + 1 + 1];/*auto gs = new Mint[N - K + 1];gs[0] = 1;for (long e = K; e; e >>= 1) {if (e & 1) {gs = fft.convolute(gs, fs);gs.length = N - K + 1;}fs = fft.square(fs);fs.length = N - K + 1;}*/auto gs = Poly(fs).log(N - K + 1);gs.x[] *= Mint(K);gs = gs.exp(N - K + 1);// \sum_{a=K}^N binom(N, a) binom(M, K) K! S(a, K) M^(N-a)auto mm = new Mint[N + 1];mm[0] = 1;foreach (i; 1 .. N + 1) {mm[i] = mm[i - 1] * M;}Mint ans;foreach (a; K .. N + 1) {Mint prod = 1;prod *= fac[N];prod *= invFac[N - a];prod *= gs[a - K];prod *= mm[N - a];ans += prod;}ans *= binom(M, K);writeln(ans);}} catch (EOFException e) {}}