This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std ;
#define int int64_t //be careful about this
#define endl "\n"
#define f(i,a,b) for(int i=int(a);i<int(b);++i)
#define pr pair
#define ar array
#define fr first
#define sc second
#define vt vector
#define pb push_back
#define eb emplace_back
#define LB lower_bound
#define UB upper_bound
#define PQ priority_queue
#define sz(x) ((int)(x).size())
#define all(a) (a).begin(),(a).end()
#define allr(a) (a).rbegin(),(a).rend()
#define mem0(a) memset(a, 0, sizeof(a))
#define mem1(a) memset(a, -1, sizeof(a))
template<class A> void rd(vt<A>& v);
template<class T> void rd(T& x){ cin >> x; }
template<class H, class... T> void rd(H& h, T&... t) { rd(h) ; rd(t...) ;}
template<class A> void rd(vt<A>& x) { for(auto& a : x) rd(a) ;}
template<class T> bool ckmin(T& a, const T& b) { return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { return a < b ? a = b, 1 : 0; }
template<typename T>
void __p(T a) {
cout<<a;
}
template<typename T, typename F>
void __p(pair<T, F> a) {
cout<<"{";
__p(a.first);
cout<<",";
__p(a.second);
cout<<"}\n";
}
template<typename T>
void __p(std::vector<T> a) {
cout<<"{";
for(auto it=a.begin(); it<a.end(); it++)
__p(*it),cout<<",}\n"[it+1==a.end()];
}
template<typename T, typename ...Arg>
void __p(T a1, Arg ...a) {
__p(a1);
__p(a...);
}
template<typename Arg1>
void __f(const char *name, Arg1 &&arg1) {
cout<<name<<" : ";
__p(arg1);
cout<<endl;
}
template<typename Arg1, typename ... Args>
void __f(const char *names, Arg1 &&arg1, Args &&... args) {
int bracket=0,i=0;
for(;; i++)
if(names[i]==','&&bracket==0)
break;
else if(names[i]=='(')
bracket++;
else if(names[i]==')')
bracket--;
const char *comma=names+i;
cout.write(names,comma-names)<<" : ";
__p(arg1);
cout<<" | ";
__f(comma+1,args...);
}
void setIO(string s = "") {
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
cin.exceptions(cin.failbit);
cout.precision(15); cout << fixed;
#ifdef ONLINE_JUDGE
if(sz(s)){
freopen((s+".in").c_str(),"r",stdin);
freopen((s+".out").c_str(),"w",stdout);
}
#define __f(...) 0
#endif
}
void err(bool flag){cout << (flag?"YES":"NO"); exit(0);}
const int MAX_N = 2 * 300000 + 1;
multiset<pr<int,int>> g[MAX_N];
vt<bool> vis(MAX_N,false);
bitset<MAX_N> is;
int tot = 0;
void dfs(int i) {
vis[i] = true;
if (!sz(g[i])) return;
auto [nxt,cost] = *g[i].begin();
tot += cost;
if (!vis[nxt]) {
g[nxt].erase(g[nxt].find({i, -cost}));
g[i].clear();
dfs(nxt);
}
}
signed main(){
setIO() ;
int n,k; rd(n,k);
f(id,0,2*n){
int l,r,s; rd(l,r,s);
--l,--r;
g[l].insert({r+n,s});
g[r+n].insert({l,-s});
}
// keep removing those with degree one.
queue<int> q;
f(i,0,2*n){
if(sz(g[i]) == 1) q.push(i);
else if(sz(g[i]) == 0) err(0);
}
while(sz(q)){
int now = q.front(); q.pop();
if(!sz(g[now])) err(0);
auto [nxt,cost] = *g[now].begin();
tot += cost;
g[now].clear();
g[nxt].erase(g[nxt].find({now,-cost}));
if(sz(g[nxt]) == 1) q.push(nxt);
}
vt<int> W;
if(tot) W.pb(abs(tot));
f(i,0,2*n) if(!vis[i] && sz(g[i])){
tot = 0;
g[i].erase(g[i].begin());
dfs(i);
if(tot) W.pb(abs(tot));
}
int sum = accumulate(all(W),0);
is[0] = true;
for(auto i : W) is |= (is << i);
f(i,0,MAX_N){
if(abs(sum - 2*i) <= k && is[i]) err(1);
}
err(0);
}
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