Problem:
Score : 400 points

Problem Statement

Kenkoooo is planning a trip in Republic of Snuke.
In this country, there are n cities and m trains running.
The cities are numbered 1 through n, and the i-th train connects City u_i and v_i bidirectionally.
Any city can be reached from any city by changing trains.

Two currencies are used in the country: yen and snuuk.
Any train fare can be paid by both yen and snuuk.
The fare of the i-th train is a_i yen if paid in yen, and b_i snuuk if paid in snuuk.

In a city with a money exchange office, you can change 1 yen into 1 snuuk.
However, when you do a money exchange, you have to change all your yen into snuuk.
That is, if Kenkoooo does a money exchange when he has X yen, he will then have X snuuk.
Currently, there is a money exchange office in every city, but the office in City i will shut down in i years and can never be used in and after that year.

Kenkoooo is planning to depart City s with 10^{15} yen in his pocket and head for City t, and change his yen into snuuk in some city while traveling.
It is acceptable to do the exchange in City s or City t.

Kenkoooo would like to have as much snuuk as possible when he reaches City t by making the optimal choices for the route to travel and the city to do the exchange.
For each i=0,...,n-1, find the maximum amount of snuuk that Kenkoooo has when he reaches City t if he goes on a trip from City s to City t after i years.
You can assume that the trip finishes within the year.

Constraints

2 \leq n \leq 10^5

1 \leq m \leq 10^5

1 \leq s,t \leq n

s \neq t

1 \leq u_i < v_i \leq n

1 \leq a_i,b_i \leq 10^9

If i\neq j, then u_i \neq u_j or v_i \neq v_j.

Any city can be reached from any city by changing trains.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

n m s t
u_1 v_1 a_1 b_1
:
u_m v_m a_m b_m

Output

Print n lines.
In the i-th line, print the maximum amount of snuuk that Kenkoooo has when he reaches City t if he goes on a trip from City s to City t after i-1 years.

Sample Input 1

4 3 2 3
1 4 1 100
1 2 1 10
1 3 20 1

Sample Output 1

999999999999998
999999999999989
999999999999979
999999999999897

After 0 years, it is optimal to do the exchange in City 1.

After 1 years, it is optimal to do the exchange in City 2.

Note that City 1 can still be visited even after the exchange office is closed.
Also note that, if it was allowed to keep 1 yen when do the exchange in City 2 and change the remaining yen into snuuk, we could reach City 3 with 999999999999998 snuuk, but this is NOT allowed.

After 2 years, it is optimal to do the exchange in City 3.

After 3 years, it is optimal to do the exchange in City 4.
Note that the same train can be used multiple times.

Sample Input 2

8 12 3 8
2 8 685087149 857180777
6 7 298270585 209942236
2 4 346080035 234079976
2 5 131857300 22507157
4 8 30723332 173476334
2 6 480845267 448565596
1 4 181424400 548830121
4 5 57429995 195056405
7 8 160277628 479932440
1 6 475692952 203530153
3 5 336869679 160714712
2 7 389775999 199123879

Sample Output 2

999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994

Solution in C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Collections;
using System.Collections.Specialized;
using System.Linq;
using System.Text;
using System.IO;
using System.Reflection;
using static System.Math;
using System.Numerics;
static class Program{
	const int mod=(int)1e9+7;
	static List<Tuple<int,int,int>>[] li;
	static void Main(){
		Sc sc=new Sc();
		int[] s=sc.Ia;
		int n=s[0],m=s[1];
		li=new List<Tuple<int,int,int>>[n+1];
		var b=new bool[n+1];
		var c1=new long[n+1];
		var c2=new long[n+1];
		for(int i=1;i<=n;i++){
			li[i]=new List<Tuple<int,int,int>>();
			c1[i]=c2[i]=long.MaxValue;
		}
		for(int i=0;i<m;i++){
			int[] e=sc.Ia;
			li[e[0]].Add(Tuple.Create(e[1],e[2],e[3]));
			li[e[1]].Add(Tuple.Create(e[0],e[2],e[3]));
		}
		var pq=new Pq<Mo<int>>(32,true);
		pq.Push(new Mo<int>(0,s[2]));
		c1[s[2]]=0;
		while(pq.cnt>0){
			var e=pq.Top;
			pq.Pop();
			if(b[e.d]){continue;}
			b[e.d]=true;
			for(int i=0;i<li[e.d].Count;i++){
				if(!b[li[e.d][i].Item1]&&c1[li[e.d][i].Item1]>li[e.d][i].Item2+e.n){
					pq.Push(new Mo<int>(li[e.d][i].Item2+e.n,li[e.d][i].Item1));
					c1[li[e.d][i].Item1]=li[e.d][i].Item2+e.n;
				}
			}
		}
		pq=new Pq<Mo<int>>(32,true);
		pq.Push(new Mo<int>(0,s[3]));
		b=new bool[n+1];
		c2[s[3]]=0;
		while(pq.cnt>0){
			var e=pq.Top;
			pq.Pop();
			if(b[e.d]){continue;}
			b[e.d]=true;
			for(int i=0;i<li[e.d].Count;i++){
				if(!b[li[e.d][i].Item1]&&c2[li[e.d][i].Item1]>li[e.d][i].Item3+e.n){
					pq.Push(new Mo<int>(li[e.d][i].Item3+e.n,li[e.d][i].Item1));
					c2[li[e.d][i].Item1]=li[e.d][i].Item3+e.n;
				}
			}
		}
		long p=long.MaxValue;
		var ans=new long[n];
		for(int i=n;i>0;i--){
			p=Min(p,c1[i]+c2[i]);
			ans[i-1]=(long)1e15-p;
		}
		Console.WriteLine(String.Join("\n",ans));
	}
}
public class Mo<T>:IComparable{
	public long n;
	public T d;
	public Mo(long n,T d){this.n=n;this.d=d;}
	public int CompareTo(object obj){
		Mo<T> mymo=(Mo<T>)obj;
		if(mymo.n>n){return -1;}
		else if(mymo.n<n){return 1;}
		else{return 0;}
	}
}
public class Pq<T> where T:IComparable{
	private T[] he;
	public int cnt=0,max=0;
	private Func<T,T,int> compare;
	public Pq(int max,bool mm){
		this.max=max;
		he=new T[max];
		if(mm){compare=Ao;}
		else{compare=Do;}
	}
	public void Push(T x){
		if(cnt==max){Extend();}
		int j=cnt;
		while(j!=0&&compare(x,he[(j-1)>>1])>0){he[j]=he[(j-1)>>1];j=(j-1)>>1;}
		he[j]=x;
		cnt++;
	}
	public void Pop(){
		cnt--;
		T r=he[cnt];
		int j=0;
		while(true){
			if(j*2+1<cnt){
				if(compare(he[j*2+1],he[j*2+2])>0){j=j*2+1;}
				else{j=j*2+2;}
			}
			else if(j*2<cnt){j=j*2+1;}
			else{break;}
			if(compare(he[j],r)<=0){j=(j-1)>>1;break;}
			he[(j-1)>>1]=he[j];
		}
		he[j]=r;
	}
	private int Ao(T x,T y){return y.CompareTo(x);}
	private int Do(T x,T y){return x.CompareTo(y);}
	public T Top{get{return he[0];}}
	private void Extend(){
		T[] nhe=new T[max<<1];
		Array.Copy(he,nhe,max);
		he=nhe;
		max<<=1;
	}
}

public class Sc{
	public int I{get{return int.Parse(Console.ReadLine());}}
	public long L{get{return long.Parse(Console.ReadLine());}}
	public double D{get{return double.Parse(Console.ReadLine());}}
	public string S{get{return Console.ReadLine();}}
	public int[] Ia{get{return Array.ConvertAll(Console.ReadLine().Split(),int.Parse);}}
	public long[] La{get{return Array.ConvertAll(Console.ReadLine().Split(),long.Parse);}}
	public double[] Da{get{return Array.ConvertAll(Console.ReadLine().Split(),double.Parse);}}
	public string[] Sa{get{return Console.ReadLine().Split();}}
	public object[] Oa{get{return Console.ReadLine().Split();}}
	public int[] Ia2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),int.Parse);}}
	public int[] Ia3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),int.Parse);}
	public int[] Ia3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),int.Parse);}
	public long[] La2{get{return Array.ConvertAll(("0 "+Console.ReadLine()+" 0").Split(),long.Parse);}}
	public long[] La3(int a){return Array.ConvertAll((a.ToString()+" "+Console.ReadLine()).Split(),long.Parse);}
	public long[] La3(bool a,int b,bool c,int d){return Array.ConvertAll(((a?b.ToString()+" ":"")+Console.ReadLine()+(c?" "+d.ToString():"")).Split(),long.Parse);}
	public T[] Arr<T>(int n,Func<T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f();}return a;}
	public T[] Arr<T>(int n,Func<int,T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i);}return a;}
	public T[] Arr<T>(int n,Func<string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(Console.ReadLine().Split());}return a;}
	public T[] Arr<T>(int n,Func<int,string[],T> f){var a=new T[n];for(int i=0;i<n;i++){a[i]=f(i,Console.ReadLine().Split());}return a;}
}