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.ArrayList;
import java.util.List;
import java.util.Scanner;
import java.util.TreeMap;



public class Main {

	public static void main(String[] args) {

		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int s = sc.nextInt()-1;
		int t = sc.nextInt()-1;

		ArrayList<Node> graph = new ArrayList<Node>();

		for (int i=0;i<n;i++) {
			graph.add(new Node());
			graph.get(i).id=i;
		}

		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();
			Edge e = new Edge();
			e.from=u;
			e.to=v;
			e.yen=a;
			e.snuke=b;
			Edge f = new Edge();
			f.from=v;
			f.to=u;
			f.yen=a;
			f.snuke=b;

			graph.get(u).edges.add(e);
			graph.get(v).edges.add(f);
		}


		TreeMap<Long,Node> map = new TreeMap<Long, Node>();
		for(int i=0;i<n;i++) {
			if (i != s) {
				graph.get(i).yen=(long)Math.pow(10, 14);

			} else {
				graph.get(i).yen=0;
			}
			map.put(graph.get(i).yen*n-Long.MAX_VALUE+i, graph.get(i));
		}


		while (!map.isEmpty()) {
			Node node = map.firstEntry().getValue();
			map.remove(map.firstEntry().getKey(), node);
			for (Edge e:node.edges) {
				Node toNode = graph.get(e.to);
				if (toNode.yen > node.yen+e.yen && map.containsKey(toNode.yen*n-Long.MAX_VALUE+toNode.id)) {
					map.remove(toNode.yen*n-Long.MAX_VALUE+toNode.id, toNode);
					toNode.yen = node.yen+e.yen;
					map.put(toNode.yen*n-Long.MAX_VALUE+toNode.id, toNode);
				}
			}
		}


		map = new TreeMap<Long, Node>();
		for(int i=0;i<n;i++) {
			if (i != t) {
				graph.get(i).snuke=(long)Math.pow(10, 14);

			} else {
				graph.get(i).snuke=0;
			}
			map.put(graph.get(i).snuke*n-Long.MAX_VALUE+i, graph.get(i));
		}

		while (!map.isEmpty()) {
			Node node = map.firstEntry().getValue();
			map.remove(map.firstEntry().getKey(), node);
			for (Edge e:node.edges) {
				Node toNode = graph.get(e.to);
				if (toNode.snuke > node.snuke+e.snuke && map.containsKey(toNode.snuke*n-Long.MAX_VALUE+toNode.id)) {
					map.remove(toNode.snuke*n-Long.MAX_VALUE+toNode.id, toNode);
					toNode.snuke = node.snuke+e.snuke;
					map.put(toNode.snuke*n-Long.MAX_VALUE+toNode.id, toNode);
				}
			}
		}

		long min = Long.MAX_VALUE;
		long[] ans = new long[n];
		for (int i=n-1;i>=0;i--) {
			min = Math.min(graph.get(i).yen+graph.get(i).snuke, min);
			ans[i] = min;
		}
		for (int i=0;i<n;i++) {
			System.out.println((long)Math.pow(10, 15)-ans[i]);
		}

	}



}


class Edge {
	int from;
	int to;
	long yen;
	long snuke;
}

class Node {
	int id;
	List<Edge> edges=new ArrayList<Edge>();
	long yen;
	long snuke;
}