結果
| 問題 |
No.1354 Sambo's Treasure
|
| コンテスト | |
| ユーザー |
 Chanyuh
|
| 提出日時 | 2021-01-20 17:15:15 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 442 ms / 2,000 ms |
| コード長 | 8,645 bytes |
| コンパイル時間 | 1,745 ms |
| コンパイル使用メモリ | 144,352 KB |
| 最終ジャッジ日時 | 2025-01-18 02:53:41 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 61 |
ソースコード
#include<iostream>
#include<array>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<complex>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<tuple>
#include<cassert>
using namespace std;
typedef long long ll;
typedef unsigned int ui;
const ll mod = 998244353;
const ll INF = (ll)1000000007 * 1000000007;
typedef pair<int, int> P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define Per(i,sta,n) for(int i=n-1;i>=sta;i--)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
typedef long double ld;
const ld eps = 1e-8;
const ld pi = acos(-1.0);
typedef pair<ll, ll> LP;
int dx[4]={1,-1,0,0};
int dy[4]={0,0,1,-1};
template<class T>bool chmax(T &a, const T &b) {if(a<b){a=b;return 1;}return 0;}
template<class T>bool chmin(T &a, const T &b) {if(b<a){a=b;return 1;}return 0;}
template<int mod>
struct ModInt {
long long x;
static constexpr int MOD = mod;
ModInt() : x(0) {}
ModInt(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
explicit operator int() const {return x;}
ModInt &operator+=(const ModInt &p) {
if((x += p.x) >= mod) x -= mod;
return *this;
}
ModInt &operator-=(const ModInt &p) {
if((x += mod - p.x) >= mod) x -= mod;
return *this;
}
ModInt &operator*=(const ModInt &p) {
x = (int)(1LL * x * p.x % mod);
return *this;
}
ModInt &operator/=(const ModInt &p) {
*this *= p.inverse();
return *this;
}
ModInt operator-() const { return ModInt(-x); }
ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }
ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }
ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }
ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }
ModInt operator%(const ModInt &p) const { return ModInt(0); }
bool operator==(const ModInt &p) const { return x == p.x; }
bool operator!=(const ModInt &p) const { return x != p.x; }
ModInt inverse() const{
int a = x, b = mod, u = 1, v = 0, t;
while(b > 0) {
t = a / b;
a -= t * b;
swap(a, b);
u -= t * v;
swap(u, v);
}
return ModInt(u);
}
ModInt power(long long n) const {
ModInt ret(1), mul(x);
while(n > 0) {
if(n & 1)
ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
ModInt power(const ModInt p) const{
return ((ModInt)x).power(p.x);
}
friend ostream &operator<<(ostream &os, const ModInt<mod> &p) {
return os << p.x;
}
friend istream &operator>>(istream &is, ModInt<mod> &a) {
long long x;
is >> x;
a = ModInt<mod>(x);
return (is);
}
};
using modint = ModInt<mod>;
struct ModFac{
public:
vector<modint> f,i_f;
int n;
ModFac(int n_){
n=n_;
f.resize(n+1,1);
i_f.resize(n+1,1);
for(int i=0;i<n;i++){
f[i+1]=f[i]*(modint)(i+1);
}
i_f[n]=f[n].power(mod-2);
for(int i=n-1;i>=0;i--){
i_f[i]=i_f[i+1]*(modint)(i+1);
}
}
ModFac(modint n_){
n=(int)n_;
f.resize(n+1,1);
i_f.resize(n+1,1);
for(int i=0;i<n;i++){
f[i+1]=f[i]*(modint)(i+1);
}
i_f[n]=f[n].power(mod-2);
for(int i=n-1;i>=0;i--){
i_f[i]=i_f[i+1]*(modint)(i+1);
}
}
modint factorial(int x){
//cout << f.size() << endl;
return f[x];
}
modint inv_factorial(int x){
return i_f[x];
}
modint comb(int m,int k){
if (m<0 or k<0) return 0;
if (m<k) return 0;
return f[m]*i_f[k]*i_f[m-k];
}
};
template <typename Mint>
struct NumberTheoreticTransformFriendlyModInt {
vector<Mint> dw, idw;
int max_base;
Mint root;
NumberTheoreticTransformFriendlyModInt() {
const unsigned mod = Mint::MOD;
assert(mod >= 3 && mod % 2 == 1);
auto tmp = mod - 1;
max_base = 0;
while(tmp % 2 == 0)
tmp >>= 1, max_base++;
root = 2;
while(root.power((mod - 1) >> 1) == 1)
root += 1;
assert(root.power(mod - 1) == 1);
dw.resize(max_base);
idw.resize(max_base);
for(int i = 0; i < max_base; i++) {
dw[i] = -root.power((mod - 1) >> (i + 2));
idw[i] = Mint(1) / dw[i];
}
}
void ntt(vector<Mint> &a) {
const int n = (int)a.size();
assert((n & (n - 1)) == 0);
assert(__builtin_ctz(n) <= max_base);
for(int m = n; m >>= 1;) {
Mint w = 1;
for(int s = 0, k = 0; s < n; s += 2 * m) {
for(int i = s, j = s + m; i < s + m; ++i, ++j) {
auto x = a[i], y = a[j] * w;
a[i] = x + y, a[j] = x - y;
}
w *= dw[__builtin_ctz(++k)];
}
}
}
void intt(vector<Mint> &a, bool f = true) {
const int n = (int)a.size();
assert((n & (n - 1)) == 0);
assert(__builtin_ctz(n) <= max_base);
for(int m = 1; m < n; m *= 2) {
Mint w = 1;
for(int s = 0, k = 0; s < n; s += 2 * m) {
for(int i = s, j = s + m; i < s + m; ++i, ++j) {
auto x = a[i], y = a[j];
a[i] = x + y, a[j] = (x - y) * w;
}
w *= idw[__builtin_ctz(++k)];
}
}
if(f) {
Mint inv_sz = Mint(1) / n;
for(int i = 0; i < n; i++)
a[i] *= inv_sz;
}
}
vector<Mint> multiply(vector<Mint> a, vector<Mint> b) {
int need = a.size() + b.size() - 1;
int nbase = 1;
while((1 << nbase) < need)
nbase++;
int sz = 1 << nbase;
a.resize(sz, 0);
b.resize(sz, 0);
ntt(a);
ntt(b);
Mint inv_sz = Mint(1) / sz;
for(int i = 0; i < sz; i++)
a[i] *= b[i] * inv_sz;
intt(a, false);
a.resize(need);
return a;
}
};
int n,m,l,k;
vector<P> cs,ts;
modint dp1[100010][110];
ModFac MF(500010);
vector<modint> calc(int s){
vector<P> vec={cs[s]};
bool f=false;
rep(i,l){
if(cs[s].first<=ts[i].first && ts[i].first<=cs[s+1].first){
if(cs[s].second<=ts[i].second && ts[i].second<=cs[s+1].second){
if(cs[s+1]==ts[i]) f=true;
if(cs[s]==ts[i] || cs[s+1]==ts[i]) continue;
vec.push_back(ts[i]);
}
}
}
vec.push_back(cs[s+1]);
int z=vec.size();
vector<vector<modint>> r(z,vector<modint>(z));
per(i,z){
Rep(j,i+1,z){
r[i][j]=MF.comb(vec[j].first-vec[i].first+vec[j].second-vec[i].second,vec[j].first-vec[i].first);
Rep(k,i+1,j){
r[i][j]-=MF.comb(vec[k].first-vec[i].first+vec[k].second-vec[i].second,vec[k].first-vec[i].first)*r[k][j];
}
}
}
vector<vector<modint>> dp2(z,vector<modint>(z+1));
//cout << z << " " << f << endl;
dp2[0][0]=1;
Rep(i,1,z){
rep(j,i){
rep(k,i+1){
dp2[i][k+1]+=r[j][i]*dp2[j][k];
}
}
// rep(k,i+2){
// cout << i << " " << k << " " << dp2[i][k] << endl;
// }
}
vector<modint> res(z+1,0);
Rep(k,1,z+1){
//cout << k << " " << dp2[z-1][k] << endl;
if(f)res[k]=dp2[z-1][k];
else res[k-1]=dp2[z-1][k];
}
return res;
}
NumberTheoreticTransformFriendlyModInt<modint> NTT;
vector<modint> mul(vector<vector<modint>> &fs,int l,int r){
if(r-l==0)return vector<modint>(1,1);
if(r-l==1)return fs[l];
return NTT.multiply(mul(fs,l,(l+r)/2),mul(fs,(l+r)/2,r));
}
void solve(){
cin >> n >> m >> l >> k;chmin(k,l);
cs.resize(m+2);ts.resize(l);
cs[0]=P(0,0);cs[m+1]=P(n,n);
rep(i,m){
cin >> cs[i+1].first >> cs[i+1].second;
}
rep(i,l){
cin >> ts[i].first >> ts[i].second;
}
sort(ts.begin(),ts.end());
vector<vector<modint>> fs;
rep(i,m+1){
fs.push_back(calc(i));
}
vector<modint> F=mul(fs,0,m+1);
modint ans=0;
rep(i,min((int)F.size(),k)+1){
ans+=F[i];
}
cout << ans << endl;
}
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
cout << fixed << setprecision(50);
solve();
}