#include using namespace std; using ll=long long; #define int ll #define rng(i,a,b) for(int i=int(a);i=int(a);i--) #define per(i,b) gnr(i,0,b) #define pb push_back #define eb emplace_back #define a first #define b second #define bg begin() #define ed end() #define all(x) x.bg,x.ed #define si(x) int(x.size()) #ifdef LOCAL #define dmp(x) cerr<<__LINE__<<" "<<#x<<" "< void chmax(t&a,u b){if(a void chmin(t&a,u b){if(b using vc=vector; template using vvc=vc>; using pi=pair; using vi=vc; template ostream& operator<<(ostream& os,const pair& p){ return os<<"{"< ostream& operator<<(ostream& os,const vc& v){ os<<"{"; for(auto e:v)os< void dmpr(ostream&os,const T&t,const Args&... args){ os< ostream& operator<<(ostream&os,const array&a){ return os<(all(a)); } template void print_tuple(ostream&,const T&){ } template void print_tuple(ostream&os,const T&t){ if(i)os<<","; os<(t); print_tuple(os,t); } template ostream& operator<<(ostream&os,const tuple&t){ os<<"{"; print_tuple<0,tuple,Args...>(os,t); return os<<"}"; } template void print(t x,int suc=1){ cout<>i; return i; } vi readvi(int n,int off=0){ vi v(n); rep(i,n)v[i]=read()+off; return v; } template void print(const vector&v,int suc=1){ rep(i,v.size()) print(v[i],i==int(v.size())-1?suc:2); } string readString(){ string s; cin>>s; return s; } template T sq(const T& t){ return t*t; } //#define CAPITAL void yes(bool ex=true){ #ifdef CAPITAL cout<<"YES"<<"\n"; #else cout<<"Yes"<<"\n"; #endif if(ex)exit(0); } void no(bool ex=true){ #ifdef CAPITAL cout<<"NO"<<"\n"; #else cout<<"No"<<"\n"; #endif if(ex)exit(0); } void possible(bool ex=true){ #ifdef CAPITAL cout<<"POSSIBLE"<<"\n"; #else cout<<"Possible"<<"\n"; #endif if(ex)exit(0); } void impossible(bool ex=true){ #ifdef CAPITAL cout<<"IMPOSSIBLE"<<"\n"; #else cout<<"Impossible"<<"\n"; #endif if(ex)exit(0); } constexpr ll ten(int n){ return n==0?1:ten(n-1)*10; } const ll infLL=LLONG_MAX/3; #ifdef int const int inf=infLL; #else const int inf=INT_MAX/2-100; #endif int topbit(signed t){ return t==0?-1:31-__builtin_clz(t); } int topbit(ll t){ return t==0?-1:63-__builtin_clzll(t); } int botbit(signed a){ return a==0?32:__builtin_ctz(a); } int botbit(ll a){ return a==0?64:__builtin_ctzll(a); } int popcount(signed t){ return __builtin_popcount(t); } int popcount(ll t){ return __builtin_popcountll(t); } bool ispow2(int i){ return i&&(i&-i)==i; } ll mask(int i){ return (ll(1)< void mkuni(vc&v){ sort(all(v)); v.erase(unique(all(v)),v.ed); } ll rand_int(ll l, ll r) { //[l, r] #ifdef LOCAL static mt19937_64 gen; #else static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count()); #endif return uniform_int_distribution(l, r)(gen); } template void myshuffle(vc&a){ rep(i,si(a))swap(a[i],a[rand_int(0,i)]); } template int lwb(const vc&v,const t&a){ return lower_bound(all(v),a)-v.bg; } //dep,par は not verified //yukicoder no.1024 template struct treedfs{ const vvc&g; const int n; int cnt; vi par,dep,in,out; void dfs(int v,int p,int d){ par[v]=p; dep[v]=d; in[v]=cnt++; for(auto e:g[v])if(e!=p) dfs(e,v,d+1); out[v]=cnt; } treedfs(const vvc&gg,int r):g(gg),n(si(g)),cnt(0),par(n),dep(n),in(n),out(n){ dfs(r,-1,0); } }; template struct BIT{ vc buf; int s; BIT(int n=0){init(n);} void init(int n){buf.assign(s=n,0);} void add(int i,t v){ for(;i=0;i-=(i+1)&(-i-1)) res+=buf[i]; return res; } t sum(int b,int e){ return get(e-1)-get(b-1); } int kth(int k){ int res=0; for(int i=topbit(s);i>=0;i--){ int w=res+(1<>n>>m; int s=n+m; vvc idx(n); rep(i,n)idx[i].pb(i); vvc t(s); rep(i,n-1)t[i].pb(i+1); vc pos(m); vi ks(m); rep(i,m){ int a,b,k;cin>>a>>b>>k; ks[i]=k; a--;b--; int cur=n+i; pos[i]=pi(a,si(idx[a])); idx[a].pb(cur); int par=idx[b].back(); t[par].pb(cur); } rep(i,s)reverse(all(t[i])); treedfs h(t,0); vi corr(s); rep(i,n)for(auto j:idx[i]) corr[h.in[j]]=i; BIT bit(s); rep(i,n)bit.add(h.in[idx[i].back()],1); //dmp(t); rep(i,m){ int a,b;tie(a,b)=pos[i]; if(b==si(idx[a])-1){ bit.add(h.in[idx[a][b]],-1); bit.add(h.in[idx[a][b-1]],1); } int j=idx[a][b]; int w=idx[a][b-1]; //dmp2(j,w); int ans=-1; vc z; z.eb(0,min(h.in[j],h.in[w]+1)); if(h.in[j]