結果
| 問題 | No.2459 Stampaholic (Hard) |
| ユーザー |
 Rubikun
|
| 提出日時 | 2023-09-13 06:15:48 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 642 ms / 4,000 ms |
| コード長 | 32,156 bytes |
| コンパイル時間 | 4,652 ms |
| コンパイル使用メモリ | 256,676 KB |
| 実行使用メモリ | 49,608 KB |
| 最終ジャッジ日時 | 2024-06-30 16:26:41 |
| 合計ジャッジ時間 | 12,700 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 43 ms
26,960 KB |
| testcase_01 | AC | 640 ms
49,228 KB |
| testcase_02 | AC | 160 ms
31,080 KB |
| testcase_03 | AC | 43 ms
26,964 KB |
| testcase_04 | AC | 43 ms
26,956 KB |
| testcase_05 | AC | 42 ms
26,964 KB |
| testcase_06 | AC | 42 ms
26,832 KB |
| testcase_07 | AC | 42 ms
26,960 KB |
| testcase_08 | AC | 277 ms
35,284 KB |
| testcase_09 | AC | 169 ms
31,780 KB |
| testcase_10 | AC | 583 ms
46,376 KB |
| testcase_11 | AC | 320 ms
37,396 KB |
| testcase_12 | AC | 629 ms
48,132 KB |
| testcase_13 | AC | 585 ms
46,276 KB |
| testcase_14 | AC | 182 ms
32,324 KB |
| testcase_15 | AC | 642 ms
48,676 KB |
| testcase_16 | AC | 640 ms
49,608 KB |
| testcase_17 | AC | 639 ms
49,224 KB |
| testcase_18 | AC | 639 ms
48,796 KB |
| testcase_19 | AC | 638 ms
49,220 KB |
| testcase_20 | AC | 40 ms
26,960 KB |
| testcase_21 | AC | 541 ms
44,260 KB |
ソースコード
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return true; } return false; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return true; } return false; }
#define all(x) (x).begin(),(x).end()
#define fi first
#define se second
#define mp make_pair
#define si(x) int(x.size())
const int mod=998244353,MAX=2000005,INF=1<<30;
// FPS 全部載せ
// from: https://gist.github.com/yosupo06/ddd51afb727600fd95d9d8ad6c3c80c9
// (based on AtCoder STL)
#include <algorithm>
#include <array>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
} // namespace internal
} // namespace atcoder
#include <utility>
namespace atcoder {
namespace internal {
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if (x < 0) x += m;
return x;
}
struct barrett {
unsigned int _m;
unsigned long long im;
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
unsigned int umod() const { return _m; }
unsigned int mul(unsigned int a, unsigned int b) const {
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x =
(unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if (_m <= v) v += _m;
return v;
}
};
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
constexpr bool is_prime_constexpr(int n) {
if (n <= 1) return false;
if (n == 2 || n == 7 || n == 61) return true;
if (n % 2 == 0) return false;
long long d = n - 1;
while (d % 2 == 0) d /= 2;
for (long long a : {2, 7, 61}) {
long long t = d;
long long y = pow_mod_constexpr(a, t, n);
while (t != n - 1 && y != 1 && y != n - 1) {
y = y * y % n;
t <<= 1;
}
if (y != n - 1 && t % 2 == 0) {
return false;
}
}
return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while (t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
constexpr int primitive_root_constexpr(int m) {
if (m == 2) return 1;
if (m == 167772161) return 3;
if (m == 469762049) return 3;
if (m == 754974721) return 11;
if (m == 998244353) return 3;
int divs[20] = {};
divs[0] = 2;
int cnt = 1;
int x = (m - 1) / 2;
while (x % 2 == 0) x /= 2;
for (int i = 3; (long long)(i)*i <= x; i += 2) {
if (x % i == 0) {
divs[cnt++] = i;
while (x % i == 0) {
x /= i;
}
}
}
if (x > 1) {
divs[cnt++] = x;
}
for (int g = 2;; g++) {
bool ok = true;
for (int i = 0; i < cnt; i++) {
if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
ok = false;
break;
}
}
if (ok) return g;
}
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int128 =
typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type,
std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value,
__uint128_t,
unsigned __int128>;
template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value &&
std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value,
make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type>::type;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<is_integral<T>::value &&
std::is_unsigned<T>::value,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T> using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <numeric>
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
static_modint(T v) {
_v = (unsigned int)(v % umod());
}
static_modint(bool v) { _v = ((unsigned int)(v) % umod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
mint& operator*=(const mint& rhs) {
unsigned long long z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
if (prime) {
assert(_v);
return pow(umod() - 2);
} else {
auto eg = internal::inv_gcd(_v, m);
assert(eg.first == 1);
return eg.second;
}
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id> struct dynamic_modint : internal::modint_base {
using mint = dynamic_modint;
public:
static int mod() { return (int)(bt.umod()); }
static void set_mod(int m) {
assert(1 <= m);
bt = internal::barrett(m);
}
static mint raw(int v) {
mint x;
x._v = v;
return x;
}
dynamic_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
dynamic_modint(T v) {
long long x = (long long)(v % (long long)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = nullptr>
dynamic_modint(T v) {
_v = (unsigned int)(v % mod());
}
dynamic_modint(bool v) { _v = ((unsigned int)(v) % mod()); }
unsigned int val() const { return _v; }
mint& operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
mint& operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
mint operator++(int) {
mint result = *this;
++*this;
return result;
}
mint operator--(int) {
mint result = *this;
--*this;
return result;
}
mint& operator+=(const mint& rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator-=(const mint& rhs) {
_v += mod() - rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
mint& operator*=(const mint& rhs) {
_v = bt.mul(_v, rhs._v);
return *this;
}
mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }
mint operator+() const { return *this; }
mint operator-() const { return mint() - *this; }
mint pow(long long n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
mint inv() const {
auto eg = internal::inv_gcd(_v, mod());
assert(eg.first == 1);
return eg.second;
}
friend mint operator+(const mint& lhs, const mint& rhs) {
return mint(lhs) += rhs;
}
friend mint operator-(const mint& lhs, const mint& rhs) {
return mint(lhs) -= rhs;
}
friend mint operator*(const mint& lhs, const mint& rhs) {
return mint(lhs) *= rhs;
}
friend mint operator/(const mint& lhs, const mint& rhs) {
return mint(lhs) /= rhs;
}
friend bool operator==(const mint& lhs, const mint& rhs) {
return lhs._v == rhs._v;
}
friend bool operator!=(const mint& lhs, const mint& rhs) {
return lhs._v != rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt = 998244353;
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
} // namespace atcoder
#include <cassert>
#include <type_traits>
#include <vector>
namespace atcoder {
namespace internal {
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i < cnt2 - 2; i++) {
sum_e[i] = es[i] * now;
now *= ies[i];
}
}
for (int ph = 1; ph <= h; ph++) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint now = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * now;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
now *= sum_e[bsf(~(unsigned int)(s))];
}
}
}
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
void butterfly_inv(std::vector<mint>& a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
if (first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for (int i = cnt2; i >= 2; i--) {
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for (int i = 0; i < cnt2 - 2; i++) {
sum_ie[i] = ies[i] * now;
now *= es[i];
}
}
for (int ph = h; ph >= 1; ph--) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint inow = 1;
for (int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for (int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] =
(unsigned long long)(mint::mod() + l.val() - r.val()) *
inow.val();
}
inow *= sum_ie[bsf(~(unsigned int)(s))];
}
}
}
} // namespace internal
template <class mint, internal::is_static_modint_t<mint>* = nullptr>
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
if (std::min(n, m) <= 60) {
if (n < m) {
std::swap(n, m);
std::swap(a, b);
}
std::vector<mint> ans(n + m - 1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) {
ans[i + j] += a[i] * b[j];
}
}
return ans;
}
int z = 1 << internal::ceil_pow2(n + m - 1);
a.resize(z);
internal::butterfly(a);
b.resize(z);
internal::butterfly(b);
for (int i = 0; i < z; i++) {
a[i] *= b[i];
}
internal::butterfly_inv(a);
a.resize(n + m - 1);
mint iz = mint(z).inv();
for (int i = 0; i < n + m - 1; i++) a[i] *= iz;
return a;
}
template <unsigned int mod = 998244353,
class T,
std::enable_if_t<internal::is_integral<T>::value>* = nullptr>
std::vector<T> convolution(const std::vector<T>& a, const std::vector<T>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
using mint = static_modint<mod>;
std::vector<mint> a2(n), b2(m);
for (int i = 0; i < n; i++) {
a2[i] = mint(a[i]);
}
for (int i = 0; i < m; i++) {
b2[i] = mint(b[i]);
}
auto c2 = convolution(move(a2), move(b2));
std::vector<T> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
c[i] = c2[i].val();
}
return c;
}
std::vector<long long> convolution_ll(const std::vector<long long>& a,
const std::vector<long long>& b) {
int n = int(a.size()), m = int(b.size());
if (!n || !m) return {};
static constexpr unsigned long long MOD1 = 754974721; // 2^24
static constexpr unsigned long long MOD2 = 167772161; // 2^25
static constexpr unsigned long long MOD3 = 469762049; // 2^26
static constexpr unsigned long long M2M3 = MOD2 * MOD3;
static constexpr unsigned long long M1M3 = MOD1 * MOD3;
static constexpr unsigned long long M1M2 = MOD1 * MOD2;
static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3;
static constexpr unsigned long long i1 =
internal::inv_gcd(MOD2 * MOD3, MOD1).second;
static constexpr unsigned long long i2 =
internal::inv_gcd(MOD1 * MOD3, MOD2).second;
static constexpr unsigned long long i3 =
internal::inv_gcd(MOD1 * MOD2, MOD3).second;
auto c1 = convolution<MOD1>(a, b);
auto c2 = convolution<MOD2>(a, b);
auto c3 = convolution<MOD3>(a, b);
std::vector<long long> c(n + m - 1);
for (int i = 0; i < n + m - 1; i++) {
unsigned long long x = 0;
x += (c1[i] * i1) % MOD1 * M2M3;
x += (c2[i] * i2) % MOD2 * M1M3;
x += (c3[i] * i3) % MOD3 * M1M2;
long long diff =
c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1));
if (diff < 0) diff += MOD1;
static constexpr unsigned long long offset[5] = {
0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3};
x -= offset[diff % 5];
c[i] = x;
}
return c;
}
} // namespace atcoder
using mint=atcoder::modint998244353;
vector<mint> prebat(vector<mint> S,int szsum){
int z = 1 << atcoder::internal::ceil_pow2(szsum-1);
auto res=S;
res.resize(z);
atcoder::internal::butterfly(res);
return res;
}
// szsum = aの配列の長さ + bの配列の長さ
vector<mint> sufbat(vector<mint> S,int szsum){
int z = 1 << atcoder::internal::ceil_pow2(szsum-1);
auto res=S;
atcoder::internal::butterfly_inv(res);
res.resize(szsum-1);
mint iz = mint(z).inv();
for (int i = 0; i < szsum - 1; i++) res[i] *= iz;
return res;
}
// szsum = aの配列の長さ + bの配列の長さ
mint inv[MAX],fac[MAX],finv[MAX];
void make(){
fac[0]=fac[1]=1;
finv[0]=finv[1]=1;
inv[1]=1;
for(int i=2;i<MAX;i++){
inv[i]=-inv[mod%i]*(mod/i);
fac[i]=fac[i-1]*i;
finv[i]=finv[i-1]*inv[i];
}
}
mint comb(ll a,ll b){
if(a<b) return 0;
return fac[a]*finv[b]*finv[a-b];
}
mint perm(ll a,ll b){
if(a<b) return 0;
return fac[a]*finv[a-b];
}
vector<mint> bibun(vector<mint> F,int deg){
vector<mint> res(deg+1);
for(int i=1;i<si(F)&&i-1<=deg;i++){
res[i-1]=F[i]*i;
}
return res;
}
vector<mint> sekibun(vector<mint> F,int deg){
vector<mint> res(deg+1);
for(int i=0;i<min(si(F),deg);i++){
res[i+1]=F[i]*inv[i+1];
}
return res;
}
vector<mint> invv(vector<mint> F,int deg){
assert(F[0]!=0);
mint kake=mint(F[0]).inv();
for(int i=0;i<si(F);i++){
F[i]*=kake;
}
vector<mint> G(1,1);
int len=1;
while(len<=deg){
vector<mint> f=F;f.resize(len*2);
vector<mint> g=G;g.resize(len*2);
atcoder::internal::butterfly(f);
atcoder::internal::butterfly(g);
for(int i=0;i<len*2;i++) f[i]*=g[i];
atcoder::internal::butterfly_inv(f);
vector<mint> nf(len*2);
for(int i=len;i<2*len;i++) nf[i-len]=f[i];
f=nf;
atcoder::internal::butterfly(f);
for(int i=0;i<len*2;i++) f[i]*=g[i];
atcoder::internal::butterfly_inv(f);
mint iz=mint(len*2).inv();
mint coe=-iz*iz;
G.resize(len*2);
for(int i=0;i<len;i++) G[len+i]=f[i]*coe;
len*=2;
}
G.resize(deg+1);
for(int i=0;i<=deg;i++) G[i]*=kake;
return G;
}//1/Tのdeg次以下を返す
vector<mint> logg(vector<mint> F,int deg){
assert(F[0]==1);
vector<mint> FF=bibun(F,deg);
vector<mint> waru=invv(F,deg);
vector<mint> G=atcoder::convolution(FF,waru);
G=sekibun(G,deg);
return G;
}
// F0 = 1
vector<mint> expp(vector<mint> F,int deg){
if(si(F)){
assert(F[0]==0);
}
vector<mint> G(1,1);
int len=1;
while(len<=deg){
vector<mint> nex=logg(G,len*2-1);
for(int i=0;i<si(nex);i++) nex[i]*=(-1);
for(int i=0;i<si(nex);i++){
if(i<si(F)) nex[i]+=F[i];
}
nex[0]++;
nex=atcoder::convolution(nex,G);
nex.resize(len*2);
len*=2;
G=nex;
}
G.resize(deg+1);
return G;
}
// F0 = 0
vector<mint> poww(vector<mint> F,int deg,ll K){
if(K==0){
vector<mint> res(deg+1);
res[0]=1;
return res;
}
if(si(F)==0){
vector<mint> res(deg+1);
return res;
}
ll geta=-1;
mint kake=0;
for(int i=0;i<si(F);i++){
if(F[i]!=0){
geta=i;
kake=F[i].inv();
break;
}
}
if(geta==-1){
vector<mint> res(deg+1);
return res;
}
if(geta>1000000000LL/K){
vector<mint> res(deg+1);
return res;
}
if(geta*K>deg){
vector<mint> res(deg+1);
return res;
}
vector<mint> nF(si(F)-geta);
for(int i=geta;i<si(F);i++){
nF[i-geta]=(F[i]*kake);
}
F=nF;
vector<mint> FF=logg(nF,deg-geta*K);
for(int i=0;i<si(FF);i++) FF[i]*=K;
vector<mint> G=expp(FF,deg-geta*K);
kake=kake.inv();
kake=kake.pow(K);
vector<mint> res(deg+1);
for(int i=0;i<si(G);i++){
res[geta*K+i]=G[i]*kake;
}
return res;
}
mint senkeizenka(vector<mint> A,vector<mint> C,ll K){
if(K<si(A)) return A[K];
int D=si(A);
assert(si(A)==si(C));
vector<mint> Q(D+1);
Q[0]=1;
for(int i=1;i<=D;i++) Q[i]=-C[i-1];
auto P=atcoder::convolution(A,Q);
P.resize(D);
while(K){
auto Qneg=Q;
for(int i=1;i<si(Qneg);i+=2) Qneg[i]=-Qneg[i];
auto x=atcoder::convolution(P,Qneg);
auto y=atcoder::convolution(Q,Qneg);
P.clear();
Q.clear();
for(int i=(K&1);i<si(x);i+=2) P.push_back(x[i]);
for(int i=0;i<si(y);i+=2) Q.push_back(y[i]);
K/=2;
}
return P[0]/Q[0];
}
//a[0],...,a[d-1]
//c[1],...,c[d]
mint senkeizenka2(vector<mint> P,vector<mint> Q,ll K){
while(K){
auto Qneg=Q;
for(int i=1;i<si(Qneg);i+=2) Qneg[i]=-Qneg[i];
auto x=atcoder::convolution(P,Qneg);
auto y=atcoder::convolution(Q,Qneg);
P.clear();
Q.clear();
for(int i=(K&1);i<si(x);i+=2) P.push_back(x[i]);
for(int i=0;i<si(y);i+=2) Q.push_back(y[i]);
K/=2;
}
return P[0]/Q[0];
}
// P/Q
// make() を呼ばないとsekibun呼ぶやつで一部バグる
// MAX=2*deg ぐらい必要な気がする
pair<vector<mint>,vector<mint>> warizan(vector<mint> P,vector<mint> Q){
if(si(P)<si(Q)) return mp(vector<mint>{},P);
auto revP=P;reverse(all(revP));
auto revQ=Q;reverse(all(revQ));
revQ=invv(revQ,si(P)-si(Q));
auto shou=atcoder::convolution(revP,revQ);
shou.resize(si(P)-si(Q)+1);
reverse(all(shou));
auto hiku=atcoder::convolution(Q,shou);
vector<mint> amari(si(P));
for(int i=0;i<si(P);i++){
amari[i]=P[i]-hiku[i];
}
while(si(shou)&&shou.back()==0) shou.pop_back();
while(si(amari)&&amari.back()==0) amari.pop_back();
return mp(shou,amari);
}
// 最高位が0でないようにしている(0のときは空)
// 多項式での除算
vector<mint> multieval(vector<mint> P,vector<mint> que){
if(si(que)==0) return {};
int N=si(que),n=1;
while(n<N) n*=2;
que.resize(n);
vector<vector<mint>> Atree(n+n-1),Btree(n+n-1);
for(int i=0;i<n;i++) Atree[n-1+i]={-que[i],1};
for(int i=n-2;i>=0;i--){
Atree[i]=atcoder::convolution(Atree[2*i+1],Atree[2*i+2]);
}
Btree[0]=warizan(P,Atree[0]).se;
for(int i=1;i<n+n-1;i++){
Btree[i]=warizan(Btree[(i-1)/2],Atree[i]).se;
}
vector<mint> res(N,0);
for(int i=0;i<N;i++){
if(si(Btree[n-1+i])) res[i]=Btree[n-1+i][0];
}
return res;
}
int main(){
std::ifstream in("text.txt");
std::cin.rdbuf(in.rdbuf());
cin.tie(0);
ios::sync_with_stdio(false);
make();
ll H,W,N,K;cin>>H>>W>>N>>K;
mint al=(H-K+1)*(W-K+1);
mint ans=H*W;
ll th,tw,cnh,cnw;
if(H<2*K){
th=H-K;
}else{
th=K-1;
}
if(W<2*K){
tw=W-K;
}else{
tw=K-1;
}
cnh=H-2*th;
cnw=W-2*tw;
vector<mint> keiH(N+1),keiW(N+1);
vector<mint> B(N+2);
{
vector<mint> A(N+2);
for(int i=0;i<=N+1;i++){
A[i]=mint(th+1).pow(i)*finv[i];
B[i]=finv[i];
}
A.erase(A.begin());
B.erase(B.begin());
B=invv(B,N);
auto C=atcoder::convolution(A,B);
C[0]--;
for(int k=0;k<=N;k++){
keiH[k]=C[k]*fac[k]*2+mint(th+1).pow(k)*cnh;
}
}
{
vector<mint> A(N+2);
for(int i=0;i<=N+1;i++){
A[i]=mint(tw+1).pow(i)*finv[i];
}
A.erase(A.begin());
auto C=atcoder::convolution(A,B);
C[0]--;
for(int k=0;k<=N;k++){
keiW[k]=C[k]*fac[k]*2+mint(tw+1).pow(k)*cnw;
}
}
al=al.inv();
for(int k=0;k<=N;k++){
if(k&1) ans+=comb(N,k)*al.pow(k)*keiH[k]*keiW[k];
else ans-=comb(N,k)*al.pow(k)*keiH[k]*keiW[k];
//cout<<keiH[k].val()<<endl;
}
cout<<ans.val()<<endl;
}