[NOI2014] 购票

#include<bits/stdc++.h>
#define For(i,a,b) for(register int i=(a);i<=(b);++i)
#define Rep(i,a,b) for(register int i=(a);i>=(b);--i)
#define int long long 
using namespace std;
inline int read()
{
    char c=getchar();int x=0;bool f=0;
    for(;!isdigit(c);c=getchar())f^=!(c^45);
    for(;isdigit(c);c=getchar())x=(x<<1)+(x<<3)+(c^48);
    if(f)x=-x;return x;
}

#define fi first
#define se second
#define pb push_back
#define mkp make_pair
typedef pair<int,int>pii;
typedef vector<int>vi;

#define maxn 200005
#define N   4000005
int n;
vector<int>e[maxn];

int k[maxn],b[maxn],cnt,rt[maxn<<2];
inline int f(int id,int x){return k[id]*x+b[id];}
int tag[N],ls[N],rs[N];
void upd(int&p,int l,int r,int x)
{
	if(!p)p=++cnt;
	if(!tag[p])return tag[p]=x,void();
	int mid=l+r>>1;
	if(f(x,mid)<f(tag[p],mid))swap(x,tag[p]);
	if(l<r) k[x]<k[tag[p]]?upd(rs[p],mid+1,r,x):upd(ls[p],l,mid,x);
}
int qry(int p,int l,int r,int x)
{
	if(!p)return 1e18;
	int mid=l+r>>1;
	return min(f(tag[p],x),x<=mid?qry(ls[p],l,mid,x):qry(rs[p],mid+1,r,x));
}

void modify(int p,int l,int r,int x,int v)
{
	upd(rt[p],0,1e6,v);
	if(l==r)return;
	int mid=l+r>>1;
	x<=mid?modify(p<<1,l,mid,x,v):modify(p<<1|1,mid+1,r,x,v);
}
int ask(int p,int l,int r,int ql,int qr,int v)
{
	if(l>=ql&&r<=qr)return qry(rt[p],0,1e6,v);
	int mid=l+r>>1,res=1e18;
	if(ql<=mid)res=min(res,ask(p<<1,l,mid,ql,qr,v));
	if(qr>mid)res=min(res,ask(p<<1|1,mid+1,r,ql,qr,v));
	return res; 
}

int o[maxn],idx;
void getO(int u){
	for(auto v:e[u])getO(v);
	o[u]=++idx;
}
int s[maxn],p[maxn],q[maxn],l[maxn],fa[maxn];
int dp[maxn],dis[maxn],top,id[maxn];
void dfs(int u)
{
	k[u]=-dis[top],b[u]=dp[u];
	id[top]=u;
	modify(1,1,n,o[u],u);
	for(auto v:e[u]){
		++top,dis[top]=dis[top-1]+s[v];
		int anc=id[lower_bound(dis,dis+top,dis[top]-l[v])-dis];
		dp[v]=ask(1,1,n,o[v],o[anc],p[v]);
		dp[v]=dp[v]+dis[top]*p[v]+q[v];
		dfs(v);
		--top;
	}
}

signed main()
{
	n=read(),read();
	For(i,2,n){
		fa[i]=read(),s[i]=read(),p[i]=read(),q[i]=read(),l[i]=read();
		e[fa[i]].pb(i);
	}
	getO(1);
	dfs(1);
	For(i,2,n)printf("%lld\n",dp[i]);
	return 0;
}