結果

問題 No.2133 Take it easy!
コンテスト
ユーザー PCTprobability
提出日時 2022-11-26 00:18:39
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
WA  
実行時間 -
コード長 7,179 bytes
コンパイル時間 3,921 ms
コンパイル使用メモリ 271,020 KB
最終ジャッジ日時 2025-02-09 01:08:45
ジャッジサーバーID
（参考情報） 		judge5 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2 WA * 1
other AC * 7 WA * 18 RE * 1
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#endif
using ll = long long;
using ld = long double;
using ull = unsigned long long;
#define endl "\n"
typedef pair<int, int> Pii;
#define REP(i, n) for (int i = 0; i < (n); ++i)
#define REP3(i, m, n) for (int i = (m); (i) < int(n); ++ (i))
#define FOR(i,a,b) for(ll i=a;i<=(ll)(b);i++)
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(x) begin(x), end(x)
#define rrep(i,a,b) for(int i=a;i>=b;i--)
#define fore(i,a) for(auto &i:a)
#define all(s) (s).begin(),(s).end()
#define drep2(i, m, n) for (int i = (m)-1; i >= (n); --i)
#define drep(i, n) drep2(i, n, 0)
#define rever(vec) reverse(vec.begin(), vec.end())
#define sor(vec) sort(vec.begin(), vec.end())
#define fi first
#define se second
#define pb push_back
#define P pair<ll,ll>
#define PQminll priority_queue<ll, vector<ll>, greater<ll>>
#define PQmaxll priority_queue<ll,vector<ll>,less<ll>>
#define PQminP priority_queue<P, vector<P>, greater<P>>
#define PQmaxP priority_queue<P,vector<P>,less<P>>
#define NP next_permutation
//const ll mod = 1000000009;
const ll mod = 998244353;
//const ll mod = 1000000007;
const ll inf = 4100000000000000000ll;
const ld eps = ld(0.00000000001);
static const long double pi = 3.141592653589793;
template<class T>void vcin(vector<T> &n){for(int i=0;i<int(n.size());i++) cin>>n[i];}
template<class T,class K>void vcin(vector<T> &n,vector<K> &m){for(int i=0;i<int(n.size());i++) cin>>n[i]>>m[i];}
template<class T>void vcout(vector<T> &n){for(int i=0;i<int(n.size());i++){cout<<n[i]<<" ";}cout<<endl;}
template<class T>void vcin(vector<vector<T>> &n){for(int i=0;i<int(n.size());i++){for(int j=0;j<int(n[i].size());j++){cin>>n[i][j];}}}
template<class T>void vcout(vector<vector<T>> &n){for(int i=0;i<int(n.size());i++){for(int j=0;j<int(n[i].size());j++){cout<<n[i][j]<<" ";}cout<<endl;}cout<<endl;}
void yes(bool a){cout<<(a?"yes":"no")<<endl;}
void YES(bool a){cout<<(a?"YES":"NO")<<endl;}
void Yes(bool a){cout<<(a?"Yes":"No")<<endl;}
void possible(bool a){ cout<<(a?"possible":"impossible")<<endl; }
void Possible(bool a){ cout<<(a?"Possible":"Impossible")<<endl; }
void POSSIBLE(bool a){ cout<<(a?"POSSIBLE":"IMPOSSIBLE")<<endl; }
template<class T>auto min(const T& a){ return *min_element(all(a)); }
template<class T>auto max(const T& a){ return *max_element(all(a)); }
template<class T,class F>void print(pair<T,F> a){cout<<a.fi<<" "<<a.se<<endl;}
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<class T> void ifmin(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
template<class T> void ifmax(T t,T u){if(t>u){cout<<-1<<endl;}else{cout<<t<<endl;}}
ll fastgcd(ll u,ll v){ll shl=0;while(u&&v&&u!=v){bool eu=!(u&1);bool ev=!(v&1);if(eu&&ev){++shl;u>>=1;v>>=1;}else if(eu&&!ev){u>>=1;}else if(!eu&&ev){v>>=1;}else if(u>=v){u=(u-v)>>1;}else{ll tmp=u;u=(v-u)>>1;v=tmp;}}return !u?v<<shl:u<<shl;}
ll modPow(ll a, ll n, ll mod) { if(mod==1) return 0;ll ret = 1; ll p = a % mod; while (n) { if (n & 1) ret = ret * p % mod; p = p * p % mod; n >>= 1; } return ret; }
vector<ll> divisor(ll x){ vector<ll> ans; for(ll i = 1; i * i <= x; i++){ if(x % i == 0) {ans.push_back(i); if(i*i!=x){ ans.push_back(x / ans[i]);}}}sor(ans); return ans; }
ll pop(ll x){return __builtin_popcountll(x);}
ll poplong(ll x){ll y=-1;while(x){x/=2;y++;}return y;}
P hyou(P a){ll x=fastgcd(abs(a.fi),abs(a.se));a.fi/=x;a.se/=x;if(a.se<0){a.fi*=-1;a.se*=-1;}return a;}
P Pplus(P a,P b){ return hyou({a.fi*b.se+b.fi*a.se,a.se*b.se});}
P Ptimes(P a,ll b){ return hyou({a.fi*b,a.se});}
P Ptimes(P a,P b){ return hyou({a.fi*b.fi,a.se*b.se});}
P Pminus(P a,P b){ return hyou({a.fi*b.se-b.fi*a.se,a.se*b.se});}
P Pgyaku(P a){ return hyou({a.se,a.fi});}
template<class T>
struct Sum{
  vector<T> data;
  Sum(const vector<T>& v):data(v.size()+1){
    for(ll i=0;i<v.size();i++) data[i+1]=data[i]+v[i];
  }
  T get(ll l,ll r) const {
    return data[r]-data[l];
  }
};
template<class T>
struct Sum2{
  vector<vector<T>> data;
  Sum2(const vector<vector<T>> &v):data(v.size()+1,vector<T>(v[0].size()+1)){
    for(int i=0;i<v.size();i++) for(int j=0;j<v[i].size();j++) data[i+1][j+1]=data[i][j+1]+v[i][j];
    for(int i=0;i<v.size();i++) for(int j=0;j<v[i].size();j++) data[i+1][j+1]+=data[i+1][j];
  }
  T get(ll x1,ll y1,ll x2,ll y2) const {
    return data[x2][y2]+data[x1][y1]-data[x1][y2]-data[x2][y1];
  }
};

void cincout(){
  ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
  cout<< fixed << setprecision(15);
}
constexpr ll MAX = 500010;
ll fac[MAX],finv[MAX],inv[MAX];
void COMinit(){
  fac[0]=fac[1]=1;
  finv[0]=finv[1]=1;
  inv[1]=1;
  for(int i=2;i<MAX;i++){
    fac[i]=fac[i-1]*i%mod;
    inv[i]=mod-inv[mod%i]*(mod/i)%mod;
    finv[i]=finv[i-1]*inv[i]%mod;
  }
}
ll binom(ll n,ll k){
  if(n<k) return 0;
  if(n<0||k<0) return 0;
  return fac[n]*(finv[k]*finv[n-k]%mod)%mod;
}
ll HOM(ll n,ll k){
  if(n==0&&k==0) return 1;
  return binom(n+k-1,k);
}
ll POM(ll n,ll k){
  if(n<k) return 0;
  return fac[n]*finv[n-k]%mod;
}
using mint = modint998244353;
mint catalan(ll n){
  return mint(binom(2*n,n))/mint(n+1);
}
mint solve(ll n,ll m,vector<ll> a,vector<ll> b){
  if(m==0){
    return catalan((n+1)/2);
  }
  map<ll,ll> even,odd;
  vector<ll> rui(n+1);
  for(int i=0;i<m;i++){
    if((a[i]+b[i])%2==0){
      return 0;
    }
    rui[a[i]]++;
    rui[b[i]+1]--;
    if(a[i]%2==0){
      even[a[i]]++;
      even[b[i]+1]++;
    }
    else{
      odd[a[i]]++;
      odd[b[i]+1]++;
    }
  }
  for(int i=1;i<=n;i++) rui[i]+=rui[i-1];
  vector<ll> c,d;
  for(auto e:even) c.pb(e.fi);
  for(auto e:odd) d.pb(e.fi);
  vector<vector<ll>> u(int(c.size())),v(int(d.size()));
  vector<ll> X(int(c.size())),Y(int(d.size()));
  for(int i=0;i+1<c.size();i++){
    for(int j=0;j+1<d.size();j++){
      if(c[i]<d[j]){
        if(d[j]<=c[i+1]) return 0;
      }
      else{
        if(c[i]<=d[j+1]) return 0;
      }
      if(c[i]<d[j]&&d[j+1]<c[i+1]){
        u[i].pb(j);
        Y[j]=1;
      }
      if(d[j]<c[i]&&c[i+1]<d[j+1]){
        v[j].pb(i);
        X[i]=1;
      }
    }
  }
  ll cnt=0;
  for(int i=0;i<n;i++) if(rui[i]==0) cnt++;
  mint ans=1;
  if(cnt%2==0) ans*=catalan(cnt/2);
  else ans*=catalan((cnt+1)/2);
  for(int i=0;i<c.size();i++){
    if(X[i]==0){
      vector<ll> A,B;
      for(auto e:u[i]){
        A.pb(d[e]-c[i]);
        B.pb(d[e+1]-c[i]-1);
      }
      ans*=solve(c[i+1]-c[i],ll(A.size()),A,B);
    }
  }
  for(int i=0;i<d.size();i++){
    if(Y[i]==0){
      vector<ll> A,B;
      for(auto e:v[i]){
        A.pb(c[e]-d[i]);
        B.pb(c[e+1]-d[i]-1);
      }
      ans*=solve(d[i+1]-d[i],ll(A.size()),A,B);
    }
  }
  return ans;
}
int main() {
  cincout();
  COMinit();
  ll n,m;
  cin>>n>>m;
  vector<ll> a,b;
  for(int i=0;i<m;i++){
    ll x,y;
    cin>>x>>y;
    x--;
    y--;
    if((x+y)%2==0){
      cout<<0<<endl;
      return 0;
    }
    if(x!=0||y!=n-1){
      a.pb(x);
      b.pb(y);
    }
  }
  mint ans=solve(n,m,a,b);
  ans*=fac[(n+1)/2];
  ans*=fac[n/2];
  cout<<ans.val()<<endl;
}
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