Problem: We have a graph with N vertices and M edges, and there are two people on the graph: Takahashi and Aoki.

The i-th edge connects Vertex U_i and Vertex V_i. The time it takes to traverse this edge is D_i minutes, regardless of direction and who traverses the edge (Takahashi or Aoki).

Takahashi departs Vertex S and Aoki departs Vertex T at the same time. Takahashi travels to Vertex T and Aoki travels to Vertex S, both in the shortest time possible. Find the number of the pairs of ways for Takahashi and Aoki to choose their shortest paths such that they never meet (at a vertex or on an edge) during the travel, modulo 10^9 + 7.

Constraints

* 1 \leq N \leq 100 000
* 1 \leq M \leq 200 000
* 1 \leq S, T \leq N
* S \neq T
* 1 \leq U_i, V_i \leq N (1 \leq i \leq M)
* 1 \leq D_i \leq 10^9 (1 \leq i \leq M)
* If i \neq j, then (U_i, V_i) \neq (U_j, V_j) and (U_i, V_i) \neq (V_j, U_j).
* U_i \neq V_i (1 \leq i \leq M)
* D_i are integers.
* The given graph is connected.

Input

Input is given from Standard Input in the following format:


N M
S T
U_1 V_1 D_1
U_2 V_2 D_2
:
U_M V_M D_M


Output

Print the answer.

Examples

Input

4 4
1 3
1 2 1
2 3 1
3 4 1
4 1 1


Output

2


Input

3 3
1 3
1 2 1
2 3 1
3 1 2


Output

2


Input

8 13
4 2
7 3 9
6 2 3
1 6 4
7 6 9
3 8 9
1 2 2
2 8 12
8 6 9
2 5 5
4 2 18
5 3 7
5 1 515371567
4 8 6


Output

6

Solution (in JAVA):

Solution:
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);
        TaskE solver = new TaskE();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskE {
        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;
            int[][] es = in.nextIntArray2D(m, 3);
            Graph g = Graph.fromEdges(n, es, true);
            long[][] dcS = g.dijkstra(S);
            long[][] dcT = g.dijkstra(T);
            long distST = dcS[0][T];
            long cntST = dcS[1][T];

            long ans = 0;

            final int mod = (int) 1e9 + 7;
            for (int v = 0; v < n; v++) {
                if (dcS[0][v] + dcT[0][v] != distST) {
                    continue;
                }
                if (dcS[0][v] == dcT[0][v]) {
                    long c = dcS[1][v] * dcT[1][v] % mod;
                    ans += c * (cntST - c) % mod;
//                dump(v);
                }
                for (Edge e : g.vertex[v].edges) {
                    final int t = e.to;
                    if (dcS[0][v] + dcT[0][t] + e.cost != distST) {
                        continue;
                    }
                    if (dcS[0][v] < dcT[0][v] && dcS[0][t] > dcT[0][t]) {
                        long c = dcS[1][v] * dcT[1][t] % mod;
                        ans += c * (cntST - c) % mod;
//                    dump(v, t);
                    }
                }
            }
            out.println((ans % mod + mod) % mod);
        }

    }

    static 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);
        }

    }

    static 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 static Graph fromEdges(int n, int[][] edges, boolean bidirectional) {
            Graph g = new Graph(n);
            g.addEdges(bidirectional, edges);
            return g;
        }

        public void addEdges(boolean bidirectional, int[]... edges) {
            for (int[] e : edges) {
                int s = e[0] - 1, t = e[1] - 1;
                long cost = e.length < 3 ? 0 : e[2];
                final int eid = this.E++;
                this.addEdge(s, t, cost, eid);
                if (bidirectional) this.addEdge(t, s, cost, eid);
            }
        }

        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;
        }

        public int[] nextIntArray(final int n) {
            final int[] res = new int[n];
            for (int i = 0; i < n; i++) {
                res[i] = nextInt();
            }
            return res;
        }

        public int[][] nextIntArray2D(final int n, final int k) {
            final int[][] res = new int[n][];
            for (int i = 0; i < n; i++) {
                res[i] = nextIntArray(k);
            }
            return res;
        }

        static class EndOfFileRuntimeException extends RuntimeException {
        }

    }

    static 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);
        }

    }
}