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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.PriorityQueue;
import java.io.IOException;
import java.io.Reader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.AbstractCollection;
import java.util.List;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyInput in = new MyInput(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskD solver = new TaskD();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskD {
        public void solve(int testNumber, MyInput in, PrintWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();
            int s = in.nextInt() - 1;
            int t = in.nextInt() - 1;

            Graph g1 = new Graph(n);
            Graph g2 = new Graph(n);

            for (int i = 0; i < m; i++) {
                int u = in.nextInt() - 1;
                int v = in.nextInt() - 1;
                int a = in.nextInt();
                int b = in.nextInt();
                g1.addEdge(u, v, a, i);
                g1.addEdge(v, u, a, i);
                g2.addEdge(u, v, b, i);
                g2.addEdge(v, u, b, i);
            }

            long[] d1 = g1.dijkstra(s)[0];
            long[] d2 = g2.dijkstra(t)[0];
            long[] ans = new long[n + 1];
            for (int i = n - 1; i >= 0; i--) {
                ans[i] = Math.max(1_000000000_000000L - (d1[i] + d2[i]), ans[i + 1]);
            }
            for (int i = 0; i < n; i++) {
                out.println(ans[i]);
            }
        }

        class Edge {
            public final int edgeId;
            public final int to;
            public long cost;

            public Edge(int to, long cost, int edgeId) {
                this.to = to;
                this.cost = cost;
                this.edgeId = edgeId;
            }


            public String toString() {
                return String.format("[Edge id=%d, to=%d, cost=%d]", edgeId, to, cost);
            }

        }

        class Vertex {
            public final int id;
            public final List<Edge> edges = new ArrayList<>();

            public Vertex(final int id) {
                this.id = id;
            }

            public void addEdge(Edge e) {
                edges.add(e);
            }

        }

        class Graph {
            int V;
            int E;
            Vertex[] vertex;

            public Graph(int V) {
                this.V = V;
                this.E = 0;
                vertex = new Vertex[V];
                for (int i = 0; i < V; i++) vertex[i] = new Vertex(i);
            }

            public void addEdge(int s, int t, long c, int edgeId) {
                vertex[s].addEdge(new Edge(t, c, edgeId));
            }

            public long[][] dijkstra(int r) {
                final int mod = (int) 1e9 + 7;

                long[] dist = new long[V];
                long[] cnt = new long[V];
                Arrays.fill(dist, Long.MAX_VALUE);
                dist[r] = 0;
                cnt[r] = 1;
                PriorityQueue<long[]> que = new PriorityQueue<>((a, b) -> Long.compare(a[0], b[0]));
                que.add(new long[]{0, r});
                while (!que.isEmpty()) {
                    long[] q = que.poll();
                    long d = q[0];
                    int v = (int) q[1];
                    if (d != dist[v]) continue;
                    for (Edge e : vertex[v].edges) {
                        if (dist[e.to] > d + e.cost) {
                            dist[e.to] = d + e.cost;
                            cnt[e.to] = 0;
                            que.add(new long[]{dist[e.to], e.to});
                        }
                        if (dist[e.to] == d + e.cost) {
                            cnt[e.to] += cnt[v];
                            if (cnt[e.to] >= mod) cnt[e.to] -= mod;
                        }
                    }
                }
                return new long[][]{dist, cnt};
            }

        }

    }

    static class MyInput {
        private final BufferedReader in;
        private static int pos;
        private static int readLen;
        private static final char[] buffer = new char[1024 * 8];
        private static char[] str = new char[500 * 8 * 2];
        private static boolean[] isDigit = new boolean[256];
        private static boolean[] isSpace = new boolean[256];
        private static boolean[] isLineSep = new boolean[256];

        static {
            for (int i = 0; i < 10; i++) {
                isDigit['0' + i] = true;
            }
            isDigit['-'] = true;
            isSpace[' '] = isSpace['\r'] = isSpace['\n'] = isSpace['\t'] = true;
            isLineSep['\r'] = isLineSep['\n'] = true;
        }

        public MyInput(InputStream is) {
            in = new BufferedReader(new InputStreamReader(is));
        }

        public int read() {
            if (pos >= readLen) {
                pos = 0;
                try {
                    readLen = in.read(buffer);
                } catch (IOException e) {
                    throw new RuntimeException();
                }
                if (readLen <= 0) {
                    throw new MyInput.EndOfFileRuntimeException();
                }
            }
            return buffer[pos++];
        }

        public int nextInt() {
            int len = 0;
            str[len++] = nextChar();
            len = reads(len, isSpace);
            int i = 0;
            int ret = 0;
            if (str[0] == '-') {
                i = 1;
            }
            for (; i < len; i++) ret = ret * 10 + str[i] - '0';
            if (str[0] == '-') {
                ret = -ret;
            }
            return ret;
        }

        public char nextChar() {
            while (true) {
                final int c = read();
                if (!isSpace[c]) {
                    return (char) c;
                }
            }
        }

        int reads(int len, boolean[] accept) {
            try {
                while (true) {
                    final int c = read();
                    if (accept[c]) {
                        break;
                    }
                    if (str.length == len) {
                        char[] rep = new char[str.length * 3 / 2];
                        System.arraycopy(str, 0, rep, 0, str.length);
                        str = rep;
                    }
                    str[len++] = (char) c;
                }
            } catch (MyInput.EndOfFileRuntimeException e) {
            }
            return len;
        }

        static class EndOfFileRuntimeException extends RuntimeException {
        }

    }
}

