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.util.stream.*;

public class Main {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt(), m = in.nextInt(), s = in.nextInt() - 1, t = in.nextInt() - 1;
		List<Grid>[] yen = new List[n], snu = new List[n];
		for(int i = 0; i < n; i++) {
			yen[i] = new ArrayList<>();
			snu[i] = new ArrayList<>();
		}
		for(int i = 0; i < m; i++) {
			int u = in.nextInt() - 1, v = in.nextInt() - 1;
			long a = in.nextLong(), b = in.nextLong();
			yen[u].add(new Grid(v, a));
			yen[v].add(new Grid(u, a));
			snu[u].add(new Grid(v, b));
			snu[v].add(new Grid(u, b));
		}
		long[] sc = Dijkstra.execute(yen, s), tc = Dijkstra.execute(snu, t);
		long[] ans = new long[sc.length];
		ans[ans.length - 1] = sc[sc.length - 1] + tc[tc.length - 1];
		for(int i = ans.length - 2; 0 <= i; i--) {
			ans[i] = Math.min(ans[i + 1], sc[i] + tc[i]);
		}
		for(long a : ans) {
			System.out.println((long)1e15 - a);
		}
	}
}

class Dijkstra {

	public static long[] execute(List<Grid>[] list, int start) {
		long[] cost = new long[list.length];
		Arrays.fill(cost, Long.MAX_VALUE / 2);
		cost[start] = 0;

		Queue<Grid> que = new PriorityQueue<>(Comparator.comparing(Grid::getCost));
		que.add(new Grid(start, 0));
		while(0 < que.size()) {
			Grid p = que.poll();
			if(cost[p.to] < p.cost) continue;
			for(Grid g : list[p.to]) {
				if(cost[p.to] + g.cost < cost[g.to]) {
					cost[g.to] = cost[p.to] + g.cost;
					que.add(new Grid(g.to, cost[g.to]));
				}
			}
		}
		return cost;
	}
}

class Grid {
	int to;
	long cost;

	public Grid(int to, long cost) {
		this.to = to;
		this.cost = cost;
	}
	public long getCost() { return this.cost; }
}
