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.

Examples

Input

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


Output

999999999999998
999999999999989
999999999999979
999999999999897


Input

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


Output

999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
999999574976994
import java.util.*;
import java.io.PrintWriter;
public class Main{
	static int n;
	public static void main(String[] args){
		Scanner sc=new Scanner(System.in);
		n=sc.nextInt();
		int m=sc.nextInt();
		int s=sc.nextInt()-1;
		int t=sc.nextInt()-1;
		ArrayList<Node>[] aedge=new ArrayList[n];
		ArrayList<Node>[] bedge=new ArrayList[n];
		for(int i=0; i<n; i++){
			aedge[i]=new ArrayList<>();
			bedge[i]=new ArrayList<>();
		}
		for(int i=0; i<m; i++){
			int u=sc.nextInt()-1;
			int v=sc.nextInt()-1;
			int a=sc.nextInt();
			int b=sc.nextInt();
			aedge[u].add(new Node(v,a));
			aedge[v].add(new Node(u,a));
			bedge[u].add(new Node(v,b));
			bedge[v].add(new Node(u,b));
		}
		long[] sfor=Dijkstra(aedge,s);
		long[] tfor=Dijkstra(bedge,t);
		
		long[] ans=new long[n];
		long hand=1000000000000000L;
		ans[n-1]=sfor[n-1]+tfor[n-1];
		for(int i=n-2; i>=0; i--){
			ans[i]=Math.min(ans[i+1],sfor[i]+tfor[i]);
		}
		PrintWriter pw=new PrintWriter(System.out);
		for(int i=0; i<n; i++){
			pw.println(hand-ans[i]);
		}
		pw.flush();
	}
	static long[] Dijkstra(ArrayList<Node>[] edge,int start){
		long[] re=new long[n];
		Arrays.fill(re,-1);
		PriorityQueue<Node> q=new PriorityQueue<>((x,y)->((x.dis-y.dis)<0?-1:1));
		q.add(new Node(start,0));
		while(!q.isEmpty()){
			Node node=q.poll();
			if(re[node.goal]!=-1) continue;
			re[node.goal]=node.dis;
			for(Node tmp:edge[node.goal]){
				if(re[tmp.goal]!=-1) continue;
				q.add(new Node(tmp.goal,node.dis+tmp.dis));
			}
		}
		return re;
	}
	static class Node{
		int goal;
		long dis;
		Node(int goal,long dis){
			this.goal=goal;
			this.dis=dis;
		}
	}
}
