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;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef pair<double,double> pdd;
typedef complex<double> cpx;
#define fastio cin.tie(0)->sync_with_stdio(0); cout.tie(0);
#define all(x) x.begin(),x.end()
#define compress(x) x.erase(unique(all(x)),x.end())
#define ff first
#define ss second
struct Edge{
ll x,t,c;
};
struct Di{
ll i,t,c,w;
bool operator < (const Di &d) const {
return w>d.w;
}
};
ll n,m,dist[2010];
vector<Edge> g[2010];
vector<pll> h[2010];
ll ccw(pll a, pll b, pll c){
ll k = (b.ff-a.ff)*(c.ss-a.ss)-(b.ss-a.ss)*(c.ff-a.ff);
return (k>0)-(k<0);
}
vector<pll> convexhull(vector<pll> &p){
ll n = p.size(),k=0;
if(n<3) return p;
if(n==3){
if(ccw(p[0],p[1],p[2])<0) reverse(all(p));
return p;
}
vector<pll> H(2*n);
sort(all(p));
for(int i=0;i<n;i++){
while(k>=2&&ccw(H[k-2],H[k-1],p[i])<0) k--;
H[k++] = p[i];
}
for(int i=n-1,t=k+1;i>0;i--){
while(k>=t&&ccw(H[k-2],H[k-1],p[i-1])<0) k--;
H[k++] = p[i-1];
}
H.resize(k-1);
return H;
}
ll inside(ll id, pll p){
ll n = (ll)h[id].size();
if(n<3) return 0;
if(ccw(h[id][0],h[id][1],p)<0) return 0;
if(ccw(h[id][0],h[id][n-1],p)>0) return 0;
int l = 1, r = n-1;
while(l+1<r){
int m = (l+r)/2;
if(ccw(h[id][0],h[id][m],p)>0) l = m;
else r = m;
}
return ccw(h[id][l],p,h[id][l+1])<=0;
}
void dijkstra(){
for(int i=1;i<=n;i++){
dist[i] = (ll)1e18;
}
for(int i=2;i<=n;i++){
h[i] = {{(ll)1e9,0},{0,(ll)1e9}};
}
dist[1] = 0;
h[1] = {{(ll)1e9,0},{0,(ll)1e9},{0,0}};
priority_queue<Di> pq;
pq.push({1,0,0,0});
while(!pq.empty()){
assert((ll)pq.size()<1e8);
cout << pq.size() << "\n";
ll c = pq.top().i, ct = pq.top().t;
ll cc = pq.top().c, cw = pq.top().w; pq.pop();
//cout << c << "\n";
//if(cw>dist[c]) continue;
dist[c] = min(dist[c],cw);
pll p = {ct,cc};
if(inside(c,p)&&c!=1) continue;
for(auto i:g[c]){
ll nx = i.x, nc = cc+i.c, nt = ct+i.t;
ll nw = nc*nt;
pll np = {nt,nc};
if(!inside(nx,np)){
//cout << nx << " " << h[nx].size() << " " << nc << " " << nt << "\n";
h[nx].push_back(np);
vector<pll> tmp = convexhull(h[nx]);
h[nx] = tmp;
pq.push({nx,nt,nc,nw});
}
}
}
}
int main(){
fastio;
cin >> n >> m;
for(int i=0;i<m;i++){
ll x,y,z,w; cin >> x >> y >> z >> w;
g[x].push_back({y,z,w});
g[y].push_back({x,z,w});
}
dijkstra();
for(int i=2;i<=n;i++){
cout << (dist[i]<(ll)1e18?dist[i]:-1) << "\n";
}
}
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