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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class Main {
    public static void main(final String[] args) {
        final FastScanner scanner = new FastScanner(System.in);
        final int n = scanner.nextInt();
        final int m = scanner.nextInt();
        final int s = scanner.nextInt();
        final int t = scanner.nextInt();

        final Map<Integer, List<Destination>> yenGraph = new HashMap<>();
        final Map<Integer, List<Destination>> sunukeGraph = new HashMap<>();
        for (int i = 0; i < m; i++) {
            final int u = scanner.nextInt();
            final int v = scanner.nextInt();
            final int a = scanner.nextInt();
            final int b = scanner.nextInt();

            yenGraph.computeIfAbsent(u, list -> new ArrayList<>()).add(new Destination(v, a));
            yenGraph.computeIfAbsent(v, list -> new ArrayList<>()).add(new Destination(u, a));
            sunukeGraph.computeIfAbsent(u, list -> new ArrayList<>()).add(new Destination(v, b));
            sunukeGraph.computeIfAbsent(v, list -> new ArrayList<>()).add(new Destination(u, b));
        }

        final long[] yenRoutes = dijkstra(yenGraph, s, n);
        final long[] sunukeRoutes = dijkstra(sunukeGraph, t, n);

        final long base = 1_000_000_000_000_000L;
        final long[] results = new long[n + 1];
        results[n] = base - yenRoutes[n] - sunukeRoutes[n];
        for (int i = n - 1; i >= 0; i--) {
            results[i] = Math.max(results[i + 1], base - yenRoutes[i] - sunukeRoutes[i]);
        }

        Arrays.stream(results, 1, n + 1)
                .forEach(System.out::println);
    }

    private static long[] dijkstra(final Map<Integer, List<Destination>> graph, final int start, final int n) {
        final long[] array = new long[n + 1];
        Arrays.fill(array, Long.MAX_VALUE);
        array[start] = 0;
        final PriorityQueue<Destination> queue = new PriorityQueue<>(Comparator.comparingLong(dest -> dest.cost));
        queue.addAll(graph.get(start));
        while (!queue.isEmpty()) {
            final Destination dest = queue.poll();
            if (dest.cost >= array[dest.to]) {
                continue;
            }
            array[dest.to] = dest.cost;
            graph.get(dest.to).stream()
                    .filter(next -> array[next.to] > next.cost + dest.cost)
                    .map(next -> new Destination(next.to, next.cost + dest.cost))
                    .forEach(queue::add);
        }
        return array;
    }

    private static class Destination {
        final int to;
        final long cost;

        Destination(final int to, final long cost) {
            this.to = to;
            this.cost = cost;
        }
    }

    private static class FastScanner {
        private final BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(final InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (final IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
    }
}
    