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 Java8 (OpenJDK 1.8.0) (judge verdict: Runtime Error)

import java.util.Arrays;
import java.util.HashSet;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Scanner;
import java.util.Set;

/**
 * 方針
 * 1. sをsrcに，aのコストでダイクストラ
 * 2. tをsrcに，bのコストでダイクストラ
 * 3. iの大きい淳に，s->i->tの中で一番小さいものを列挙する
 * 
 * @author "Haruhisa Ishida<haruhisa.ishida@gmail.com>"
 *
 */
public class Main {
	public static class Edge implements Comparable<Edge> {
		public int src, dst, cost;

		public Edge(int src, int dst, int cost) {
			this.src = src;
			this.dst = dst;
			this.cost = cost;
		}

		@Override
		public int compareTo(Edge arg0) {
			if (this.cost < arg0.cost) {
				return -1;
			} else if (this.cost > arg0.cost) {
				return 1;
			} else {
				return 0;
			}
		}
	}

	int n, m, s, t;
	int[] u, v, a, b;
	int[][] aDist, bDist;
	int[] srcDistances, dstDistances;
	long[] score;

	public void showScore() {
		for (int i = 0; i < n; ++i) {
			System.out.println(score[i]);
		}
	}

	public void calcScore() {
		score = new long[n];
		score[n - 1] = 1000000000000000L - srcDistances[n - 1] - dstDistances[n - 1];
		for (int i = n - 2; i >= 0; --i) {
			if (score[i + 1] > 1000000000000000L - srcDistances[i] - dstDistances[i]) {
				score[i] = score[i + 1];
			} else {
				score[i] = 1000000000000000L - srcDistances[i] - dstDistances[i];
			}
		}
	}

	public void calcDistances() {
		srcDistances = new int[n];
		Arrays.fill(srcDistances, Integer.MAX_VALUE);
		srcDistances[s - 1] = 0;
		Set<Integer> calced = new HashSet<>();
		calced.add(s - 1);

		Queue<Edge> edges = new PriorityQueue<Edge>();
		for (int i = 0; i < n; ++i) {
			if (aDist[s - 1][i] > 0) {
				edges.add(new Edge(s - 1, i, aDist[s - 1][i]));
			}
		}

		while (!edges.isEmpty()) {
			Edge edge = edges.poll();
			if (srcDistances[edge.src] + edge.cost < srcDistances[edge.dst]) {
				srcDistances[edge.dst] = srcDistances[edge.src] + edge.cost;
				calced.add(edge.dst);
			}
			for (int i = 0; i < n; ++i) {
				if (aDist[edge.dst][i] > 0) {
					if (!calced.contains(i)) {
						edges.add(new Edge(edge.dst, i, aDist[edge.dst][i]));
					}
				}
			}
		}

		dstDistances = new int[n];
		Arrays.fill(dstDistances, Integer.MAX_VALUE);
		dstDistances[t - 1] = 0;
		calced.clear();
		calced.add(t - 1);

		edges.clear();
		for (int i = 0; i < n; ++i) {
			if (bDist[t - 1][i] > 0) {
				edges.add(new Edge(t - 1, i, bDist[t - 1][i]));
			}
		}

		while (!edges.isEmpty()) {
			Edge edge = edges.poll();
			if (dstDistances[edge.src] + edge.cost < dstDistances[edge.dst]) {
				dstDistances[edge.dst] = dstDistances[edge.src] + edge.cost;
				calced.add(edge.dst);
			}
			for (int i = 0; i < n; ++i) {
				if (bDist[edge.dst][i] > 0) {
					if (!calced.contains(i)) {
						edges.add(new Edge(edge.dst, i, bDist[edge.dst][i]));
					}
				}
			}
		}

	}

	public Main(Scanner in) {
		String[] tokens = in.nextLine().split(" ");
		n = Integer.parseInt(tokens[0]);
		m = Integer.parseInt(tokens[1]);
		s = Integer.parseInt(tokens[2]);
		t = Integer.parseInt(tokens[3]);

		u = new int[m];
		v = new int[m];
		a = new int[m];
		b = new int[m];
		for (int i = 0; i < m; ++i) {
			tokens = in.nextLine().split(" ");
			u[i] = Integer.parseInt(tokens[0]);
			v[i] = Integer.parseInt(tokens[1]);
			a[i] = Integer.parseInt(tokens[2]);
			b[i] = Integer.parseInt(tokens[3]);
		}

		aDist = new int[n][n];
		bDist = new int[n][n];
		for (int i = 0; i < n; ++i) {
			for (int j = 0; j < n; ++j) {
				aDist[i][j] = 0;
				bDist[i][j] = 0;
			}
		}
		for (int i = 0; i < m; ++i) {
			int src = u[i] - 1;
			int dst = v[i] - 1;
			int costA = a[i];
			int costB = b[i];
			aDist[src][dst] = costA;
			aDist[dst][src] = costA;
			bDist[src][dst] = costB;
			bDist[dst][src] = costB;
		}
	}

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		Main ins = new Main(in);
		ins.calcDistances();
		ins.calcScore();
		ins.showScore();
		in.close();
	}

}