結果

問題 No.1523 +/- Tree
ユーザー PCTprobabilityPCTprobability
提出日時 2021-05-28 22:36:33
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 3 ms / 2,000 ms
コード長 12,635 bytes
コンパイル時間 24,594 ms
コンパイル使用メモリ 362,732 KB
最終ジャッジ日時 2025-01-21 20:12:11
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 2
other AC * 44
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 # 

#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#pragma GCC optimize("Ofast")
#include <bits/stdc++.h>
#include <unistd.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 = long long;
#define endl "\n"
#define REP3(i, m, n) for (int i = (m); (i) < int(n); ++ (i))
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define ALL(x) begin(x), end(x)
#define all(s) (s).begin(),(s).end()
//#define rep2(i, m, n) for (int i = (m); i < (n); ++i)
//#define rep(i, n) rep2(i, 0, n)
#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 REP(i, n) for (int i = 0; i < (n); ++i)
#define in scanner.read_int()
//const ll mod = 998244353;
const ll mod = 1000000007;
const ll inf = 4500000000000000000ll;
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;}}
template<typename T,typename ...Args>auto make_vector(T x,int arg,Args ...args){if constexpr(sizeof...(args)==0)return vector<T>(arg,x);else return vector(arg,make_vector<T>(x,args...));}
ll modPow(ll a, ll n, ll mod) { 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; }
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];
  }
};
class Scanner {
    vector<char> buffer;
    ssize_t n_written;
    ssize_t n_read;

public:
    Scanner(): buffer(1024*1024) { do_read(); }

    int64_t read_int() {
        int64_t ret = 0, sgn = 1;
        int ch = current_char();
        while (isspace(ch)) { ch = next_char(); }
        if (ch == '-') { sgn = -1; ch = next_char(); }
        for (; isdigit(ch); ch = next_char())
            ret = (ret * 10) + (ch - '0');
        return sgn * ret;
    }

private:
    void do_read() {
        ssize_t r = read(0, &buffer[0], buffer.size());
        if (r < 0) {
            throw runtime_error(strerror(errno));
        }
        n_written = r;
        n_read = 0;
    }

    inline int next_char() {
        ++n_read;
        if (n_read == n_written) { do_read(); }
        return current_char();
    }

    inline int current_char() {
        return (n_read == n_written) ? EOF : buffer[n_read];
    }
};

//Scanner scanner;
//void vin(vector<ll> &n){for(int i=0;i<int(n.size());i++) n[i]=in;}

void cincout(){
  ios::sync_with_stdio(false);
    std::cin.tie(nullptr);
  cout<< fixed << setprecision(20);
}
template<class T>
vector<T> NTT(vector<T> a,vector<T> b){
  ll nmod=T::mod();
  int n=a.size();
  int m=b.size();
  vector<int> x1(n);
  vector<int> y1(m);
  for(int i=0;i<n;i++){
    ll tmp1,tmp2,tmp3;
    tmp1=a[i].val();
    x1[i]=tmp1;
  }
  for(int i=0;i<m;i++){
    ll tmp1,tmp2,tmp3;
    tmp1=b[i].val();
    y1[i]=tmp1;
  }
  auto z1=convolution<167772161>(x1,y1);
  auto z2=convolution<469762049>(x1,y1);
  auto z3=convolution<1224736769>(x1,y1);
  vector<T> res(n+m-1);
  ll m1=167772161;
  ll m2=469762049;
  ll m3=1224736769;
  ll m1m2=104391568;
  ll m1m2m3=721017874;
  ll mm12=m1*m2%nmod;
  for(int i=0;i<n+m-1;i++){
    int v1=(z2[i]-z1[i])*m1m2%m2;
    if(v1<0) v1+=m2;
    int v2=(z3[i]-(z1[i]+v1*m1)%m3)*m1m2m3%m3;
    if(v2<0) v2+=m3;
    res[i]=(z1[i]+v1*m1+v2*mm12);
  }
  return res;
}
template<class T>
struct FormalPowerSeries:vector<T>{
  using vector<T>::vector;
  using vector<T>::operator=;
  using F=FormalPowerSeries;
  F operator-() const{
    F res(*this);
    for(auto &e:res) e=-e;
    return res;
  }
  F &operator*=(const T &g){
    for(auto &e:*this) e*=g;
    return *this;
  }
  F &operator/=(const T &g){
    assert(g!=T(0));
    *this*=g.inv();
    return *this;
  }
  F &operator+=(const F &g){
    int n=(*this).size(),m=g.size();
    for(int i=0;i<min(n,m);i++){
      (*this)[i]+=g[i];
    }
    return *this;
  }
  F &operator-=(const F &g){
    int n=(*this).size(),m=g.size();
    for(int i=0;i<min(n,m);i++){
      (*this)[i]-=g[i];
    }
    return *this;
  }
  F &operator<<=(const int d) {
    int n=(*this).size();
    (*this).insert((*this).begin(),d,0);
    (*this).resize(n);
    return *this;
  }
  F &operator>>=(const int d) {
    int n=(*this).size();
    (*this).erase((*this).begin(),(*this).begin()+min(n, d));
    (*this).resize(n);
    return *this;
  }
  F inv(int d=-1) const{
    int n=(*this).size();
    assert(n!=0&&(*this)[0]!=0);
    if(d==-1) d=n;
    assert(d>0);
    F res{(*this)[0].inv()};
    while(res.size()<d){
      int m=size(res);
      F f(begin(*this),begin(*this)+min(n,2*m));
      F r(res);
      f.resize(2*m);
      r.resize(2*m);
      vector<T> s=NTT(f,r);
      s.resize(2*m);
      for(int i=0;i<2*m;i++){
        s[i]=-s[i];
      }
      s[0]+=2;
      vector<T> g=NTT(s,r);
      g.resize(2*m);
      res=g;
    }
    res.resize(n);
    return res;
  }
  F &operator/=(const F &g){
    int n=(*this).size();
    *this=NTT(*this,g.inv());
    (*this).resize(n);
    return (*this);
  }
  F &operator*=(const F &g){
    int n=(*this).size();
    *this=NTT(*this,g);
    for(int i=n;i<(*this).size();i++){
      (*this)[i%n]+=(*this)[i];
    }
    (*this).resize(n);
    return (*this);
  }
  void onemul(const int d,const T c){
    int n=(*this).size();
    for(int i=n-d-1;i>=0;i--){
      (*this)[i+d]+=(*this)[i]*c;
    }
  }
  void onediv(const int d,const T c){
    int n=(*this).size();
    for(int i=0;i<n-d;i++){
      (*this)[i+d]-=(*this)[i]*c;
    }
  }
void spacemul(vector<pair<int, T>> g) {
    int n = (*this).size();
    auto [d, c] = g.front();
    if (d == 0) g.erase(g.begin());
    else c = 0;
    for(int i=n-1;i>=0;i--){
      (*this)[i] *= c;
      for (auto &[j, b] : g) {
        if (j > i) break;
        (*this)[i] += (*this)[i-j] * b;
      }
    }
  }
  void spacediv(vector<pair<int, T>> g) {
    int n = (*this).size();
    auto [d, c] = g.front();
    assert(d == 0 && c != T(0));
    T ic = c.inv();
    g.erase(g.begin());
    for(int i=0;i<n;i++){
      for (auto &[j, b] : g) {
        if (j > i) break;
        (*this)[i] -= (*this)[i-j] * b;
      }
      (*this)[i] *= ic;
    }
  }
  T eval(const T &a) const {
    T x(1),res(0);
    for(auto e:*this) res+=e*x,x*=a;
    return res;
  }
  F differential() const {
    int n=(*this).size();
    F res(n);
    for(int i=0;i<n-1;i++){
      res[i]=T(i+1)*(*this)[i+1];
    }
    res[n-1]=0;
    return res;
  }
  F Integral() const {
    int n=(*this).size();
    F res(n);
    for(int i=1;i<n;i++){
      res[i]=(*this)[i-1]/T(i);
    }
    res[0]=0;
    return res;
  }
  F log() const{
    int n=(*this).size();
    F u=(*this).differential();
    F d=(*this);
    u/=d;
    u=u.Integral();
    u.resize(n);
    return u;
  }
  F exp(int d=-1) const{
    int n=(*this).size();
    assert(n!=0&&(*this)[0]==0);
    if(d==-1) d=n;
    assert(d>0);
    F res{1};
    while(res.size()<d){
      int m=size(res);
      F f(begin(*this),begin(*this)+min(n,2*m));
      F r(res);
      f.resize(2*m);
      r.resize(2*m);
      r=r.log();
      f-=r;
      f[0]++;
      F g=f*res;
      g.resize(2*m);
      res=g;
    }
    res.resize(n);
    return res;
  }
  F pow(int a){
    int n=(*this).size();
    F res(n);
    for(int i=0;i<n;i++){
      res[i]=(*this)[i];
    }
    if(a==0){
      F s(n);
      if(n>0){
        s[0]=T(1);
      }
      for(int i=0;i<n;i++){
      res[i]=s[i];
      }
      return res;
    }
    int l=0;
    while(l<n&&res[l]==0) l++;
    if(l>(n-1)/a||l==n){
      F s(n);
      for(int i=0;i<n;i++){
        res[i]=s[i];
      }
      return res;
    }
    T t=res[l];
    res.erase(res.begin(),res.begin()+l);
    res/=t;
    F g=res.log();
    for(int i=0;i<n;i++){
      res[i]=g[i];
    }
    res*=a;
    g=res.exp();
    for(int i=0;i<n;i++){
      res[i]=g[i];
    }
    res*=t.pow(a);
    res.insert(res.begin(),l*a,0);
    return res;
  }
  F sqrt(int k=-1){
    int n=(*this).size();
    if(k==-1){
      k=n;
    }
    ll m=T::mod();
    if((*this)[0]==T(0)){
      for(int i=1;i<int((*this).size());i++){
        if((*this)[i]!=T(0)){
          if(i&1) return {};
          if(n-i/2<=0)break;
          auto ret=(*this>>i).sqrt(n-i/2)<<(i/2);
          if(int(ret.size())<n) return {};
          return ret;
        }
      }
      F g(n);
      for(int i=0;i<n;i++){
        g[i]=0;
      }
      return g;
    }
    else{
      if(modsqrt((*this)[0].val(),m)==-1){
        return {};
      }
      F ret{T(modsqrt((*this)[0].val(),m))};
      for(int i=1;i<n;i<<=1){
        ret.resize(2*i);
        ret=(ret+(*this)/ret);
        ret/=T(2);
      }
      return ret;
    }
  }
  F operator*(const T &g) const { return F(*this)*=g;}
  F operator-(const T &g) const { return F(*this)-=g;}
  F operator*(const F &g) const { return F(*this)*=g;}
  F operator-(const F &g) const { return F(*this)-=g;}
  F operator+(const F &g) const { return F(*this)+=g;}
  F operator/(const F &g) const { return F(*this)/=g;}
  F operator<<(const int d) const { return F(*this)<<=d;}
  F operator>>(const int d) const { return F(*this)>>=d;}  
};
using mint=modint1000000007;
using fps = FormalPowerSeries<mint>;
using sfps = vector<pair<int, mint>>;
fps fpspow(fps a,ll n){
  ll m=a.size();
  fps ret(m);
  ret[0]=1;
  while(n){
    if(n&1){
      ret*=a;
    }
    a*=a;
    n/=2;
  }
  return ret;
}
int main() {
  cincout();
  ll a,b;
  cin>>a>>b;
  if(b==1){
    cout<<"No"<<endl;
    return 0;
  }
  if(b==2){
    if(a%2==0){
      cout<<"Yes"<<endl;
      ll tmp=1000000000-1;
      ll tmp2=-1000000000;
      for(int i=1;i<=a-1;i++){
        if(i%2) cout<<i<<" "<<i+1<<" "<<tmp<<endl;
        else cout<<i<<" "<<i+1<<" "<<tmp2<<endl;
      }
      return 0;
    }
    cout<<"No"<<endl;
    return 0;
  }
  if(b>=4){
    if(b==a-1){
      cout<<"No"<<endl;
      return 0;
    }
    cout<<"Yes"<<endl;
    cout<<1<<" "<<2<<" "<<1<<endl;
    for(int i=2;i<=b;i++){
      cout<<i<<" "<<i+1<<" "<<-1<<endl;
    }
    for(int i=b+2;i<=a;i++){
      cout<<3<<" "<<i<<" "<<1000000000<<endl;
    }
    return 0;
  }
  if(a==4){
    cout<<"No"<<endl;
    return 0;
  }
  cout<<"Yes"<<endl;
  cout<<1<<" "<<2<<" "<<-2<<endl;
  cout<<2<<" "<<3<<" "<<-2<<endl;
  for(int i=4;i<=a;i++){
    cout<<1<<" "<<i<<" "<<3<<endl;
  }
}
0