結果
| 問題 | No.1321 塗るめた |
| ユーザー |
👑  hos.lyric
|
| 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 root
class 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) const
if (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)^K
auto 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) {
}
}