結果
| 問題 |
No.1321 塗るめた
|
| コンテスト | |
| ユーザー |
 carrot46
|
| 提出日時 | 2020-12-18 00:38:54 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 503 ms / 2,000 ms |
| コード長 | 14,988 bytes |
| コンパイル時間 | 2,163 ms |
| コンパイル使用メモリ | 183,432 KB |
| 実行使用メモリ | 30,944 KB |
| 最終ジャッジ日時 | 2024-09-21 08:45:06 |
| 合計ジャッジ時間 | 13,274 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
（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
#include <bits/stdc++.h>
//#include <chrono>
//#pragma GCC optimize("O3")
using namespace std;
#define reps(i,s,n) for(int i = s; i < n; i++)
#define rep(i,n) reps(i,0,n)
#define Rreps(i,n,e) for(int i = n - 1; i >= e; --i)
#define Rrep(i,n) Rreps(i,n,0)
#define ALL(a) a.begin(), a.end()
using ll = long long;
using vec = vector<ll>;
using mat = vector<vec>;
ll N,M,H,W,Q,K,A,B;
string S;
using P = pair<ll, ll>;
const ll INF = (1LL<<60);
template<class T> bool chmin(T &a, const T &b){
if(a > b) {a = b; return true;}
else return false;
}
template<class T> bool chmax(T &a, const T &b){
if(a < b) {a = b; return true;}
else return false;
}
template<class T> void my_printv(std::vector<T> v,bool endline = true){
if(!v.empty()){
for(std::size_t i{}; i<v.size()-1; ++i) std::cout<<v[i]<<" ";
std::cout<<v.back();
}
if(endline) std::cout<<std::endl;
}
struct edge{
int to, cost;
edge(int a, int b) : to(a), cost(b){}
};
using ve = vector<edge>;
template <unsigned long long mod > class modint{
public:
ll x;
constexpr modint(){x = 0;}
constexpr modint(ll _x) : x((_x < 0 ? ((_x += (LLONG_MAX / mod) * mod) < 0 ? _x + (LLONG_MAX / mod) * mod : _x) : _x)%mod){}
constexpr modint set_raw(ll _x){
//_x in [0, mod)
x = _x;
return *this;
}
constexpr modint operator-(){
return x == 0 ? 0 : mod - x;
}
constexpr modint& operator+=(const modint& a){
if((x += a.x) >= mod) x -= mod;
return *this;
}
constexpr modint operator+(const modint& a) const{
return modint(*this) += a;
}
constexpr modint& operator-=(const modint& a){
if((x -= a.x) < 0) x += mod;
return *this;
}
constexpr modint operator-(const modint& a) const{
return modint(*this) -= a;
}
constexpr modint& operator*=(const modint& a){
(x *= a.x)%=mod;
return *this;
}
constexpr modint operator*(const modint& a) const{
return modint(*this) *= a;
}
constexpr modint pow(unsigned long long pw) const{
modint res(1), comp(*this);
while(pw){
if(pw&1) res *= comp;
comp *= comp;
pw >>= 1;
}
return res;
}
//以下、modが素数のときのみ
constexpr modint inv() const{
if(x == 2) return (mod + 1) >> 1;
return modint(*this).pow(mod - 2);
}
constexpr modint& operator/=(const modint &a){
(x *= a.inv().x)%=mod;
return *this;
}
constexpr modint operator/(const modint &a) const{
return modint(*this) /= a;
}
constexpr bool sqrt(bool find_mini = false) {
if(x == 0) return true;
modint jge = this->pow((mod - 1)>>1);
if(jge.x + 1 == mod) return false;
if((mod&3) == 3){
*this = this->pow((mod + 1)>>2);
}else{
int m = 0;
modint c, t;
if(mod == 998244353){
m = 23; c = 15311432; t = this->pow(119);
*this = this->pow(60);
}else{
ll q = mod - 1;
modint z = 2;
while(!(q&1)){q>>=1; ++m;}
while(z.pow((mod-1)>>1).x == 1) z += 1;
c = z.pow(q); t = this->pow(q);
*this = this->pow((q+1)>>1);
}
while(t.x != 1){
modint cpy_t = t;
int pw = m;
while(cpy_t.x != 1){--pw; cpy_t *= cpy_t;}
rep(i, pw-1) c *= c;
(*this) *= c;
c *= c;
t *= c;
m -= pw;
}
}
if(find_mini) this->x = min(this->x, (ll)mod - this->x);
return true;
}
};
#define mod1 998244353
using mint = modint<mod1>;
ostream& operator<<(ostream& os, const mint& a){
os << a.x;
return os;
}
using vm = vector<mint>;
class NTT{
static int root;
static vector<int> id;
static void make_bit_reverse(int n){
//n must be 2^k
int sz = id.size(), _chk = n;
while(_chk > 1){assert(!(_chk&1)); _chk>>=1;}
if(n > sz) {
id.resize(n);
while (sz < n) {
rep(i, sz) {
id[i] <<= 1;
id[i | sz] = id[i] | 1;
}
sz <<= 1;
}
}
if(n < sz){
int k = 1;
while(n * k < sz) k <<= 1;
for(int i = 1, cpy = k; cpy < sz; ++i, cpy += k) id[i] = id[cpy];
id.resize(n);
}
}
static void dft(vm &f, bool inv, int n = INT_MAX){
if(n > (int)f.size()) n = f.size();
make_bit_reverse(n);
rep(i, n) if (i > id[i]) swap(f[i], f[id[i]]);
int l{1};
for (int len = 1; len < n; ++l, len <<= 1) {
mint root_diff = mint(root).pow(inv ? (mod1 - 1) - ((mod1 - 1)>>l) : ((mod1 - 1)>>l));
int len2 = len << 1;
for (int i = 0; i < n; i += len2) {
mint z = 1;
reps(j, i, i + len) {
mint z_f = z * f[j + len];
f[j + len] = f[j] - z_f;
f[j] += z_f;
z *= root_diff;
}
}
}
if(inv) {
mint n_inv = mint(n).inv();
rep(i, n) f[i] *= n_inv;
}
}
public:
static void dft_2D(int n, int m, vector<vm> &a, bool inv){
//簡単に、書き換える形で
//aがn×mサイズであることや、n,mが2冪であることは仮定
rep(i, n) dft(a[i], inv);
rep(j, m){
vm temp(n);
rep(i, n) temp[i] = a[i][j];
dft(temp, inv);
rep(i, n) a[i][j] = temp[i];
}
}
static vm convolution(vm g, vm h){
int sz = g.size() + h.size() - 1, n = 1;
while(sz > n) n *= 2;
g.resize(n); h.resize(n);
dft(g, false); dft(h, false);
rep(i, n) g[i] *= h[i];
dft(g, true);
g.resize(sz);
return g;
}
static vm simple_pow(vm &a, ll pw){
int sz = a.size(), n = 1;
while(sz > n) n <<= 1;
n <<= 1;
vm res(n, 0), cpy(n, 0);
res[0] = 1;
copy(ALL(a), cpy.begin());
while(pw){
dft(cpy, false);
if(pw&1){
dft(res, false);
rep(i, n) res[i] *= cpy[i];
dft(res, true);
reps(i, n / 2, n) res[i] = 0;
}
rep(i, n) cpy[i] *= cpy[i];
dft(cpy, true);
reps(i, n / 2, n) cpy[i] = 0;
pw >>= 1;
}
res.resize(sz);
return res;
}
static vm inversion(vm f){
assert(f[0].x != 0);
int n = 1, sz = 1, first_sz = f.size();
while(first_sz > n) n <<= 1;
f.resize(n);
vm g(n), cpy_f(n<<1), cpy_g(n<<1);
g[0] = f[0].inv();
while(sz < n){
sz <<= 1;
copy(f.begin(), f.begin() + sz, cpy_f.begin());
copy(g.begin(), g.begin() + sz, cpy_g.begin());
dft(cpy_f, false, sz<<1);
dft(cpy_g, false, sz<<1);
rep(i, sz<<1) cpy_f[i] *= cpy_g[i] * cpy_g[i];
dft(cpy_f, true, sz<<1);
rep(i, sz) (g[i] += g[i])-= cpy_f[i];
}
g.resize(first_sz);
return g;
}
static void differential(vm &f){
int n = f.size();
rep(i, n - 1) f[i] = f[i + 1] * (i + 1);
f[n-1] = 0;
}
static void integral(vm &f){
int n = f.size();
Rreps(i, n, 1) f[i] = f[i - 1];
f[0] = 0;
mint fct(1);
reps(i, 1, n){f[i] *= fct; fct*=i;}
fct = fct.inv();
Rreps(i, n, 1){f[i] *= fct; fct*=i;}
}
static vm log(vm f){
assert(f[0].x == 1);
vm res = inversion(f);
differential(f);
res = convolution(f, res);
res.resize((int)f.size());
integral(res);
return res;
}
static vm exp(vm f){
assert(f[0].x == 0);
int n = 1, sz = 1, first_sz = f.size();
while(first_sz > n) n <<= 1;
f.resize(n);
vm g(1, 1), log_g;
while(sz < n){
sz <<= 1;
g.resize(sz);
reps(i, sz>>1, sz) g[i] = 0;
log_g = log(g);
rep(i, sz) log_g[i] = f[i] - log_g[i];
log_g[0] += 1;
g = convolution(g, log_g);
}
g.resize(first_sz);
return g;
}
static vm pow(vm f, ll pw_int){
int n = f.size(), non_zero_id{0};
mint pw(pw_int);
vm res(n, 0);
if(pw_int == 0){
res[0] = 1;
return res;
}
while(non_zero_id < n && f[non_zero_id].x == 0) ++non_zero_id;
if((n + pw_int - 1) / pw_int <= non_zero_id) return res;
mint d = f[non_zero_id], d_inv = d.inv();
rep(i, n - non_zero_id) f[i] = f[i + non_zero_id] * d.inv();
non_zero_id *= pw_int;
d = d.pow(pw_int%(mod1 - 1));
f.resize(n - non_zero_id);
res = log(f);
for(auto &e : res) e *= pw;
res = exp(res);
res.resize(n);
Rrep(i, n) res[i] = (i >= non_zero_id ? res[i - non_zero_id] * d : 0);
return res;
}
static vm geometric_series(vm f){
assert(f[0].x == 0);
f[0] = 1;
reps(i, 1, (int)f.size()) if(f[i].x) f[i].set_raw(mod1 - f[i].x);
return inversion(f);
}
static vm sqrt(vm f, bool &suc){
suc = true;
int n = 1, sz = 1, first_sz = f.size(), non_zero_id{0};
vm g(1, 1);
while(non_zero_id < first_sz && f[non_zero_id].x == 0){
++non_zero_id;
if(non_zero_id == first_sz) return vm(first_sz, 0);
if(f[non_zero_id].x != 0){suc = false; return g;}
++non_zero_id;
}
if(non_zero_id >= first_sz)return vm(first_sz, 0);
mint sq = f[non_zero_id], div = sq.inv();
if(!sq.sqrt(true)){suc = false; return g;}
rep(i, first_sz - non_zero_id) f[i] = f[i+non_zero_id] * div;
reps(i, first_sz - non_zero_id, first_sz) f[i] = 0;
non_zero_id >>= 1;
while(first_sz > n) n <<= 1;
f.resize(n);
vm cpy_f, g_inv;
while(sz < n){
sz<<=1;
g.resize(sz); cpy_f.resize(sz);
g_inv = inversion(g);
copy(f.begin(), f.begin() + sz, cpy_f.begin());
g_inv = convolution(cpy_f, g_inv);
rep(i, sz) {
g[i] += g_inv[i];
if(g[i].x&1) g[i].set_raw((g[i].x + mod1)>>1);
else g[i].set_raw(g[i].x>>1);
}
}
g.resize(first_sz);
Rreps(i, first_sz, non_zero_id) g[i] = g[i - non_zero_id] * sq;
rep(i, non_zero_id) g[i] = 0;
return g;
}
/* 未完成
static vm composition(vm f, vm g){
assert(g[0].x == 0);
int first_sz = min(f.size(), g.size()), n = 1, k = 0;
while(first_sz > n) {n <<= 1; ++k;}
{
int lb = (1 << (k >> 1)) / k, ub = (1 << ((k + 1) >> 1)) + 1;
while (ub - lb > 1) {int cen = (ub + lb) >> 1; (cen * cen * k <= n ? lb : ub) = cen;}
rep(i, n){
chmax(lb, i + 1);
if(g[i].x != 0) break;
if(i == n - 1){
vm res(first_sz, 0);
res[0] = f[0];
return res;
}
}
k = 1;
while(k < lb) k <<= 1;
if(k > n) k = n;
}
vm p(n<<1), p_prime_inv(k), q(n<<1), qpow, res, temp(n<<1);
vector<vm> dp(n);
f.resize(n); g.resize(n);
reps(i, first_sz, n) f[i] = g[i] = 0;
copy(g.begin(), g.begin() + min(k, (int)g.size()), p.begin());
copy(g.begin(), g.begin() + min(k, (int)g.size()), p_prime_inv.begin());
copy(g.begin() + k, g.end(), q.begin());
dft(q, false);
qpow = q;
dft(p, false, k<<1);
rep(i, n) dp[i].push_back(f[i]);
auto calc = [&](vm &s, vm &t){
assert((int)t.size() <= k && (int)s.size() <= k);
t.resize(k<<1);
dft(t, false);
rep(j, k<<1) t[j] *= p[j];
dft(t, true);
rep(j, (int)s.size()) t[j] += s[j];
if(t.size() > n) t.resize(n);
return t;
};
for(int cmp = 1; cmp < n; cmp <<= 1){
for(int i = 0; i < n; i += (cmp<<1)){
dp[i] = calc(dp[i], dp[i + cmp]);
dp[i + cmp].clear();
}
if((cmp<<1) != n){
rep(i, k<<1) p[i] *= p[i];
dft(p, true, k<<1);
if(k < n) k <<= 1;
else {reps(i, n, n<<1) p[i] = 0;}
dft(p, false, k<<1);
}
}
res = dp[0]; res.resize(first_sz);
k = p_prime_inv.size();
dp[0].resize(n<<1);
dft(dp[0], false);
differential(p_prime_inv);
p_prime_inv = inversion(p_prime_inv);
p_prime_inv.resize(n<<1);
dft(p_prime_inv, false);
for(int i = k; i < n; i += k){
rep(j, n<<1) dp[0][j] *= p_prime_inv[j];
dft(dp[0], true);
mint i_inv = mint(i / k).inv();
rep(j, n) dp[0][j] *= i_inv;
reps(j, n, n<<1) dp[0][j] = 0;
differential(dp[0]);
dft(dp[0], false);
copy(dp[0].begin(), dp[0].end(), temp.begin());
rep(j, n<<1) {
temp[j] *= qpow[j];
qpow[j] *= q[j];
}
dft(temp, true);
reps(j, i, first_sz) res[j] += temp[j-i];
dft(qpow, true);
reps(j, n, n<<1) qpow[j] = 0;
dft(qpow, false);
}
return res;
}
*/
};
int NTT::root = 3;
vector<int> NTT::id(1, 0);
const ll MAX_N = ll(4e+5) + 10;
vm fact(MAX_N, mint(1)), fact_inv(MAX_N, mint(1)), n_inv(MAX_N, mint(1));
void makefact(){
mint tmp;
reps(i,2,MAX_N) fact[i] = fact[i-1] * tmp.set_raw(i);
fact_inv[MAX_N - 1] = fact[MAX_N - 1].inv();
Rreps(i, MAX_N - 1, 1){
fact_inv[i] = fact_inv[i + 1] * tmp.set_raw(i + 1);
n_inv[i + 1] = fact[i] * fact_inv[i + 1];
}
}
mint nCm(ll n, ll m){
return fact[n] * fact_inv[n-m] * fact_inv[m];
}
mint nCm_inv(ll n, ll m){
return fact[n-m] * fact[m] * fact_inv[n];
}
int main(){
cin.tie(nullptr);
ios::sync_with_stdio(false);
makefact();
cin>>N>>M>>K;
vm Kcolor_in_i(N - K + 1);
mint res(0), mpow(1), M_C_K = nCm(M, K);
rep(i, N - K + 1) Kcolor_in_i[i] = fact_inv[i + 1];
Kcolor_in_i = NTT::pow(Kcolor_in_i, K);
rep(i, N - K + 1) Kcolor_in_i[i] *= fact[i + K];
Rreps(i, N + 1, K){
res += nCm(N, i) * mpow * Kcolor_in_i[i - K] * M_C_K;
mpow *= M;
}
cout<<res<<endl;
}