結果
| 問題 | No.2983 Christmas Color Grid (Advent Calender ver.) |
| ユーザー |
 tko919
|
| 提出日時 | 2024-12-08 03:45:09 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 2 ms / 3,340 ms |
| コード長 | 20,476 bytes |
| コンパイル時間 | 5,450 ms |
| コンパイル使用メモリ | 318,616 KB |
| 実行使用メモリ | 5,248 KB |
| 最終ジャッジ日時 | 2024-12-08 03:45:17 |
| 合計ジャッジ時間 | 7,321 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 64 |
ソースコード
#line 1 "library/Template/template.hpp"
#include <bits/stdc++.h>
using namespace std;
#define rep(i, a, b) for (int i = (int)(a); i < (int)(b); i++)
#define rrep(i, a, b) for (int i = (int)(b)-1; i >= (int)(a); i--)
#define ALL(v) (v).begin(), (v).end()
#define UNIQUE(v) sort(ALL(v)), (v).erase(unique(ALL(v)), (v).end())
#define SZ(v) (int)v.size()
#define MIN(v) *min_element(ALL(v))
#define MAX(v) *max_element(ALL(v))
#define LB(v, x) int(lower_bound(ALL(v), (x)) - (v).begin())
#define UB(v, x) int(upper_bound(ALL(v), (x)) - (v).begin())
using uint = unsigned int;
using ll = long long int;
using ull = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
const int inf = 0x3fffffff;
const ll INF = 0x1fffffffffffffff;
template <typename T> inline bool chmax(T &a, T b) {
if (a < b) {
a = b;
return 1;
}
return 0;
}
template <typename T> inline bool chmin(T &a, T b) {
if (a > b) {
a = b;
return 1;
}
return 0;
}
template <typename T, typename U> T ceil(T x, U y) {
assert(y != 0);
if (y < 0)
x = -x, y = -y;
return (x > 0 ? (x + y - 1) / y : x / y);
}
template <typename T, typename U> T floor(T x, U y) {
assert(y != 0);
if (y < 0)
x = -x, y = -y;
return (x > 0 ? x / y : (x - y + 1) / y);
}
template <typename T> int popcnt(T x) {
return __builtin_popcountll(x);
}
template <typename T> int topbit(T x) {
return (x == 0 ? -1 : 63 - __builtin_clzll(x));
}
template <typename T> int lowbit(T x) {
return (x == 0 ? -1 : __builtin_ctzll(x));
}
template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << "P(" << p.first << ", " << p.second << ")";
return os;
}
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) {
os << "{";
for (int i = 0; i < vec.size(); i++) {
os << vec[i] << (i + 1 == vec.size() ? "" : ", ");
}
os << "}";
return os;
}
template <typename T, typename U>
ostream &operator<<(ostream &os, const map<T, U> &map_var) {
os << "{";
for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
os << "(" << itr->first << ", " << itr->second << ")";
itr++;
if (itr != map_var.end())
os << ", ";
itr--;
}
os << "}";
return os;
}
template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var) {
os << "{";
for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
os << *itr;
++itr;
if (itr != set_var.end())
os << ", ";
itr--;
}
os << "}";
return os;
}
#ifdef LOCAL
#define show(...) _show(0, #__VA_ARGS__, __VA_ARGS__)
#else
#define show(...) true
#endif
template <typename T> void _show(int i, T name) {
cerr << '\n';
}
template <typename T1, typename T2, typename... T3>
void _show(int i, const T1 &a, const T2 &b, const T3 &...c) {
for (; a[i] != ',' && a[i] != '\0'; i++)
cerr << a[i];
cerr << ":" << b << " ";
_show(i + 1, a, c...);
}
#line 2 "library/Utility/fastio.hpp"
#include <unistd.h>
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memmove(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
pil = 0;
if (pir < SZ)
ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd(char &c) {
do {
if (pil + 1 > pir)
load();
c = ibuf[pil++];
} while (isspace(c));
}
void rd(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir)
load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir)
load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T> void rd_real(T &x) {
string s;
rd(s);
x = stod(s);
}
template <typename T> void rd_integer(T &x) {
if (pil + 100 > pir)
load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') {
minus = 1, c = ibuf[pil++];
}
}
x = 0;
while ('0' <= c) {
x = x * 10 + (c & 15), c = ibuf[pil++];
}
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (minus)
x = -x;
}
}
void rd(int &x) {
rd_integer(x);
}
void rd(ll &x) {
rd_integer(x);
}
void rd(i128 &x) {
rd_integer(x);
}
void rd(uint &x) {
rd_integer(x);
}
void rd(ull &x) {
rd_integer(x);
}
void rd(u128 &x) {
rd_integer(x);
}
void rd(double &x) {
rd_real(x);
}
void rd(long double &x) {
rd_real(x);
}
template <class T, class U> void rd(pair<T, U> &p) {
return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T> void rd_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
rd(x);
rd_tuple<N + 1>(t);
}
}
template <class... T> void rd(tuple<T...> &tpl) {
rd_tuple(tpl);
}
template <size_t N = 0, typename T> void rd(array<T, N> &x) {
for (auto &d : x)
rd(d);
}
template <class T> void rd(vector<T> &x) {
for (auto &d : x)
rd(d);
}
void read() {}
template <class H, class... T> void read(H &h, T &...t) {
rd(h), read(t...);
}
void wt(const char c) {
if (por == SZ)
flush();
obuf[por++] = c;
}
void wt(const string s) {
for (char c : s)
wt(c);
}
void wt(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++)
wt(s[i]);
}
template <typename T> void wt_integer(T x) {
if (por > SZ - 100)
flush();
if (x < 0) {
obuf[por++] = '-', x = -x;
}
int outi;
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + por, pre.num[x], 4);
por += 4;
} else if (x >= 100) {
memcpy(obuf + por, pre.num[x] + 1, 3);
por += 3;
} else if (x >= 10) {
int q = (x * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (x - q * 10) | '0';
por += 2;
} else
obuf[por++] = x | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T> void wt_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
wt(s);
}
void wt(int x) {
wt_integer(x);
}
void wt(ll x) {
wt_integer(x);
}
void wt(i128 x) {
wt_integer(x);
}
void wt(uint x) {
wt_integer(x);
}
void wt(ull x) {
wt_integer(x);
}
void wt(u128 x) {
wt_integer(x);
}
void wt(double x) {
wt_real(x);
}
void wt(long double x) {
wt_real(x);
}
template <class T, class U> void wt(const pair<T, U> val) {
wt(val.first);
wt(' ');
wt(val.second);
}
template <size_t N = 0, typename T> void wt_tuple(const T t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) {
wt(' ');
}
const auto x = std::get<N>(t);
wt(x);
wt_tuple<N + 1>(t);
}
}
template <class... T> void wt(tuple<T...> tpl) {
wt_tuple(tpl);
}
template <class T, size_t S> void wt(const array<T, S> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i)
wt(' ');
wt(val[i]);
}
}
template <class T> void wt(const vector<T> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i)
wt(' ');
wt(val[i]);
}
}
void print() {
wt('\n');
}
template <class Head, class... Tail> void print(Head &&head, Tail &&...tail) {
wt(head);
if (sizeof...(Tail))
wt(' ');
print(forward<Tail>(tail)...);
}
void __attribute__((destructor)) _d() {
flush();
}
} // namespace fastio
using fastio::flush;
using fastio::print;
using fastio::read;
inline void first(bool i = true) {
print(i ? "first" : "second");
}
inline void Alice(bool i = true) {
print(i ? "Alice" : "Bob");
}
inline void Takahashi(bool i = true) {
print(i ? "Takahashi" : "Aoki");
}
inline void yes(bool i = true) {
print(i ? "yes" : "no");
}
inline void Yes(bool i = true) {
print(i ? "Yes" : "No");
}
inline void No() {
print("No");
}
inline void YES(bool i = true) {
print(i ? "YES" : "NO");
}
inline void NO() {
print("NO");
}
inline void Yay(bool i = true) {
print(i ? "Yay!" : ":(");
}
inline void Possible(bool i = true) {
print(i ? "Possible" : "Impossible");
}
inline void POSSIBLE(bool i = true) {
print(i ? "POSSIBLE" : "IMPOSSIBLE");
}
/**
* @brief Fast IO
*/
#line 3 "sol.cpp"
#line 2 "library/Math/fastdiv.hpp"
struct FastDiv{
using u64=uint64_t;
using u128=__uint128_t;
constexpr FastDiv():m(),s(),x(){}
constexpr FastDiv(int _m)
:m(_m),s(__lg(m-1)),x(((u128(1)<<(s+64))+m-1)/m){}
constexpr int get(){return m;}
constexpr friend u64 operator/(u64 n,const FastDiv& d){
return (u128(n)*d.x>>d.s)>>64;
}
constexpr friend int operator%(u64 n,const FastDiv& d){
return n-n/d*d.m;
}
constexpr pair<u64,int> divmod(u64 n)const{
u64 q=n/(*this);
return {q,n-q*m};
}
int m,s; u64 x;
};
/**
* @brief Fast Division
*/
#line 3 "library/Math/dynamic.hpp"
struct Fp {
using u64 = uint64_t;
uint v;
static int get_mod() {
return _getmod();
}
static void set_mod(int _m) {
bar = FastDiv(_m);
}
Fp inv() const {
int tmp, a = v, b = get_mod(), x = 1, y = 0;
while (b) {
tmp = a / b, a -= tmp * b;
swap(a, b);
x -= tmp * y;
swap(x, y);
}
if (x < 0) {
x += get_mod();
}
return x;
}
Fp() : v(0) {}
Fp(ll x) {
v = x % get_mod();
if (v < 0)
v += get_mod();
}
Fp operator-() const {
return Fp() - *this;
}
Fp pow(ll t) {
assert(t >= 0);
Fp res = 1, b = *this;
while (t) {
if (t & 1)
res *= b;
b *= b;
t >>= 1;
}
return res;
}
Fp &operator+=(const Fp &x) {
v += x.v;
if (v >= get_mod())
v -= get_mod();
return *this;
}
Fp &operator-=(const Fp &x) {
v += get_mod() - x.v;
if (v >= get_mod())
v -= get_mod();
return *this;
}
Fp &operator*=(const Fp &x) {
v = (u64(v) * x.v) % bar;
return *this;
}
Fp &operator/=(const Fp &x) {
(*this) *= x.inv();
return *this;
}
Fp operator+(const Fp &x) const {
return Fp(*this) += x;
}
Fp operator-(const Fp &x) const {
return Fp(*this) -= x;
}
Fp operator*(const Fp &x) const {
return Fp(*this) *= x;
}
Fp operator/(const Fp &x) const {
return Fp(*this) /= x;
}
bool operator==(const Fp &x) const {
return v == x.v;
}
bool operator!=(const Fp &x) const {
return v != x.v;
}
friend istream &operator>>(istream &is, Fp &x) {
return is >> x.v;
}
friend ostream &operator<<(ostream &os, const Fp &x) {
return os << x.v;
}
private:
static FastDiv bar;
static int _getmod() {
return bar.get();
}
};
FastDiv Fp::bar(998244353);
void rd(Fp &x) {
fastio::rd(x.v);
}
void wt(Fp x) {
fastio::wt(x.v);
}
/**
* @brief Dynamic Modint
*/
#line 2 "library/Math/comb.hpp"
template <typename T> T Inv(ll n) {
static int md;
static vector<T> buf({0, 1});
if (md != T::get_mod()) {
md = T::get_mod();
buf = vector<T>({0, 1});
}
assert(n > 0);
n %= md;
while (SZ(buf) <= n) {
int k = SZ(buf), q = (md + k - 1) / k;
buf.push_back(buf[k * q - md] * q);
}
return buf[n];
}
template <typename T> T Fact(ll n, bool inv = 0) {
static int md;
static vector<T> buf({1, 1}), ibuf({1, 1});
if (md != T::get_mod()) {
md = T::get_mod();
buf = ibuf = vector<T>({1, 1});
}
assert(n >= 0 and n < md);
while (SZ(buf) <= n) {
buf.push_back(buf.back() * SZ(buf));
ibuf.push_back(ibuf.back() * Inv<T>(SZ(ibuf)));
}
return inv ? ibuf[n] : buf[n];
}
template <typename T> T nPr(int n, int r, bool inv = 0) {
if (n < 0 || n < r || r < 0)
return 0;
return Fact<T>(n, inv) * Fact<T>(n - r, inv ^ 1);
}
template <typename T> T nCr(int n, int r, bool inv = 0) {
if (n < 0 || n < r || r < 0)
return 0;
return Fact<T>(n, inv) * Fact<T>(r, inv ^ 1) * Fact<T>(n - r, inv ^ 1);
}
// sum = n, r tuples
template <typename T> T nHr(int n, int r, bool inv = 0) {
return nCr<T>(n + r - 1, r - 1, inv);
}
// sum = n, a nonzero tuples and b tuples
template <typename T> T choose(int n, int a, int b) {
if (n == 0)
return !a;
return nCr<T>(n + b - 1, a + b - 1);
}
/**
* @brief Combination
*/
#line 2 "library/DataStructure/unionfind.hpp"
struct UnionFind{
vector<int> par; int n;
UnionFind(){}
UnionFind(int _n):par(_n,-1),n(_n){}
int root(int x){return par[x]<0?x:par[x]=root(par[x]);}
bool same(int x,int y){return root(x)==root(y);}
int size(int x){return -par[root(x)];}
bool unite(int x,int y){
x=root(x),y=root(y); if(x==y)return false;
if(size(x)>size(y))swap(x,y);
par[y]+=par[x]; par[x]=y; n--; return true;
}
};
/**
* @brief Union Find
*/
#line 7 "sol.cpp"
using P = pair<int, int>;
map<P, vector<int>> mp = {
{{1, 1}, {0, 1}},
{{1, 2}, {0, 2, 1}},
{{1, 3}, {0, 5, 2, 1}},
{{1, 4}, {0, 12, 5, 2, 1}},
{{1, 5}, {0, 28, 12, 5, 2, 1}},
{{1, 6}, {0, 64, 28, 12, 5, 2, 1}},
{{1, 7}, {0, 144, 64, 28, 12, 5, 2, 1}},
{{1, 8}, {0, 320, 144, 64, 28, 12, 5, 2, 1}},
{{1, 9}, {0, 704, 320, 144, 64, 28, 12, 5, 2, 1}},
{{1, 10}, {0, 1536, 704, 320, 144, 64, 28, 12, 5, 2, 1}},
{{1, 11}, {0, 3328, 1536, 704, 320, 144, 64, 28, 12, 5, 2, 1}},
{{1, 12}, {0, 7168, 3328, 1536, 704, 320, 144, 64, 28, 12, 5, 2, 1}},
{{1, 13}, {0, 15360, 7168, 3328, 1536, 704, 320, 144, 64, 28, 12, 5, 2, 1}},
{{1, 14},
{0, 32768, 15360, 7168, 3328, 1536, 704, 320, 144, 64, 28, 12, 5, 2, 1}},
{{1, 15},
{0, 69632, 32768, 15360, 7168, 3328, 1536, 704, 320, 144, 64, 28, 12, 5, 2,
1}},
{{1, 16},
{0, 147456, 69632, 32768, 15360, 7168, 3328, 1536, 704, 320, 144, 64, 28,
12, 5, 2, 1}},
{{1, 17},
{0, 311296, 147456, 69632, 32768, 15360, 7168, 3328, 1536, 704, 320, 144,
64, 28, 12, 5, 2, 1}},
{{1, 18},
{0, 655360, 311296, 147456, 69632, 32768, 15360, 7168, 3328, 1536, 704,
320, 144, 64, 28, 12, 5, 2, 1}},
{{1, 19},
{0, 1376256, 655360, 311296, 147456, 69632, 32768, 15360, 7168, 3328,
1536, 704, 320, 144, 64, 28, 12, 5, 2, 1}},
{{1, 20}, {0, 2883584, 1376256, 655360, 311296, 147456, 69632,
32768, 15360, 7168, 3328, 1536, 704, 320,
144, 64, 28, 12, 5, 2, 1}},
{{1, 21}, {0, 6029312, 2883584, 1376256, 655360, 311296, 147456, 69632,
32768, 15360, 7168, 3328, 1536, 704, 320, 144,
64, 28, 12, 5, 2, 1}},
{{1, 22},
{0, 12582912, 6029312, 2883584, 1376256, 655360, 311296, 147456,
69632, 32768, 15360, 7168, 3328, 1536, 704, 320,
144, 64, 28, 12, 5, 2, 1}},
{{1, 23},
{0, 26214400, 12582912, 6029312, 2883584, 1376256, 655360, 311296,
147456, 69632, 32768, 15360, 7168, 3328, 1536, 704,
320, 144, 64, 28, 12, 5, 2, 1}},
{{1, 24}, {0, 54525952, 26214400, 12582912, 6029312, 2883584, 1376256,
655360, 311296, 147456, 69632, 32768, 15360, 7168,
3328, 1536, 704, 320, 144, 64, 28,
12, 5, 2, 1}},
{{1, 25},
{0, 113246208, 54525952, 26214400, 12582912, 6029312, 2883584,
1376256, 655360, 311296, 147456, 69632, 32768, 15360,
7168, 3328, 1536, 704, 320, 144, 64,
28, 12, 5, 2, 1}},
{{2, 2}, {0, 8, 4, 4, 1}},
{{2, 3}, {0, 40, 17, 14, 10, 6, 1}},
{{2, 4}, {0, 192, 80, 64, 39, 28, 20, 8, 1}},
{{2, 5}, {0, 896, 368, 296, 184, 120, 81, 58, 34, 10, 1}},
{{2, 6}, {0, 4096, 1664, 1344, 856, 560, 368, 240, 167, 112, 52, 12, 1}},
{{2, 7},
{0, 18432, 7424, 6016, 3904, 2568, 1712, 1112, 728, 488, 337, 198, 74, 14,
1}},
{{2, 8},
{0, 81920, 32768, 26624, 17536, 11584, 7816, 5136, 3384, 2208, 1456, 992,
647, 324, 100, 16, 1}},
{{2, 9},
{0, 360448, 143360, 116736, 77824, 51584, 35136, 23304, 15520, 10232, 6704,
4392, 2936, 1976, 1169, 498, 130, 18, 1}},
{{2, 10}, {0, 1572864, 622592, 507904, 342016, 227328, 156032,
104256, 70024, 46640, 30888, 20320, 13304, 8784,
5904, 3792, 1991, 728, 164, 20, 1}},
{{2, 11},
{0, 6815744, 2686976, 2195456, 1490944, 993280, 686080, 461184,
311872, 209416, 139968, 93048, 61440, 40328, 26480, 17624,
11672, 6952, 3217, 1022, 202, 22, 1}},
{{2, 12}, {0, 29360128, 11534336, 9437184, 6455296, 4308992, 2992128,
2021376, 1374592, 929088, 625544, 419408, 279656, 185376,
122088, 80112, 52888, 35200, 22416, 12160, 4967,
1388, 244, 24, 1}},
{{3, 3}, {0, 400, 144, 106, 84, 69, 52, 32, 9, 1}},
{{3, 4}, {0, 3840, 1360, 952, 705, 550, 445, 360, 270, 164, 62, 12, 1}},
{{3, 5},
{0, 35840, 12544, 8720, 6408, 4897, 3772, 2972, 2371, 1873, 1385, 854, 376,
101, 15, 1}},
{{3, 6},
{0, 327680, 113664, 78592, 57936, 44456, 34161, 26334, 20329, 15846, 12510,
9758, 7131, 4478, 2164, 714, 149, 18, 1}},
{{3, 7}, {0, 2949120, 1015808, 699392, 516864, 398928, 308296, 238385,
183352, 140476, 108244, 84130, 65926, 50898, 36946, 23558,
12123, 4602, 1205, 206, 21, 1}},
{{3, 8}, {0, 26214400, 8978432, 6160384, 4561920, 3537664, 2748496,
2136040, 1652625, 1269794, 973997, 746362, 574842, 446028,
347449, 266040, 192322, 124150, 66909, 28072, 8654,
1876, 272, 24, 1}},
{{4, 4},
{0, 73728, 25600, 17152, 11728, 9040, 7504, 6288, 5340, 4436, 3432, 2360,
1296, 492, 116, 16, 1}},
{{4, 5}, {0, 1376256, 471040, 314368, 213248, 158976, 128272,
105936, 89480, 75998, 64363, 53486, 42473, 31078,
19942, 10358, 3972, 1054, 186, 20, 1}},
{{4, 6}, {0, 25165824, 8519680, 5668864, 3856384, 2863104, 2288896,
1868032, 1553240, 1299184, 1090650, 919360, 774295, 643000,
517972, 394544, 274893, 167464, 83894, 32492, 9316,
1920, 272, 24, 1}},
{{5, 5}, {0, 51380224, 17301504, 11501568, 7749632, 5599232, 4361216,
3564416, 3023760, 2603088, 2265120, 1971974, 1703398, 1448460,
1194986, 939036, 687581, 454452, 258314, 119182, 42437,
11295, 2192, 296, 25, 1}}};
int main() {
int H, W;
ll K, mod;
read(H, W, K, mod);
if(H>W)swap(H,W);
Fp::set_mod(mod);
vector<Fp> pw(H * W + 2);
rep(x, 1, H * W + 1) pw[x] = Fp(x).pow(K);
Fp ret;
auto cnt=mp[{H,W}];
rep(x,1,H*W+1)ret+=pw[x]*cnt[x];
Fp sub;
rep(x, 1, H * W + 1) sub += Inv<Fp>(x);
ret *= sub;
ret /= Fp(2).pow(H * W);
print(ret);
return 0;
}