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.OutputStream;
import java.io.PrintStream;
import java.io.IOException;
import java.util.TreeSet;
import java.util.ArrayList;
import java.io.UncheckedIOException;
import java.util.List;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            BAvoidingCollision solver = new BAvoidingCollision();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class BAvoidingCollision {
        Modular mod = new Modular(1e9 + 7);
        long inf = (long) 1e18;
        Debug debug = new Debug(false);

        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            int m = in.readInt();

            Node[] nodes = new Node[n];

            for (int i = 0; i < n; i++) {
                nodes[i] = new Node();
                nodes[i].id = i;
            }

            Node s = nodes[in.readInt() - 1];
            Node t = nodes[in.readInt() - 1];

            Edge[] edges = new Edge[m];
            for (int i = 0; i < m; i++) {
                Edge e = new Edge();
                e.a = nodes[in.readInt() - 1];
                e.b = nodes[in.readInt() - 1];
                e.len = in.readInt();
                e.a.adj.add(e);
                e.b.adj.add(e);
                edges[i] = e;
            }

            dijkstra(nodes, s, 0);
            dijkstra(nodes, t, 1);

            long best = t.dists[0];
            int sum = 0;

            //vertex
            for (Node node : nodes) {
                if (node.dists[0] + node.dists[1] != best ||
                        node.dists[0] != node.dists[1]) {
                    continue;
                }
                int local = mod.mul(node.ways[0], node.ways[1]);
                local = mod.mul(local, local);
                sum = mod.plus(sum, local);
            }

            //edge
            for (Edge e : edges) {
                if (e.a.dists[0] > e.b.dists[0]) {
                    Node tmp = e.a;
                    e.a = e.b;
                    e.b = tmp;
                }

                if (e.a.dists[0] + e.b.dists[1] + e.len != best) {
                    continue;
                }

                if (e.a.dists[0] >= e.b.dists[1] + e.len || e.b.dists[1] >= e.a.dists[0] + e.len) {
                    continue;
                }
                int local = mod.mul(e.a.ways[0], e.b.ways[1]);
                local = mod.mul(local, local);
                sum = mod.plus(sum, local);
            }

            int ans = mod.mul(t.ways[0], s.ways[1]);
            debug.debug("ans", ans);
            debug.debug("sum", sum);
            ans = mod.subtract(ans, sum);


            out.println(ans);
        }

        public void dijkstra(Node[] nodes, Node s, int i) {
            for (Node node : nodes) {
                node.ways[i] = 0;
                node.dists[i] = inf;
            }
            s.dists[i] = 0;
            s.ways[i] = 1;
            TreeSet<Node> pq = new TreeSet<>((a, b) -> a.dists[i] == b.dists[i] ? Integer.compare(a.id, b.id) : Long.compare(a.dists[i], b.dists[i]));

            pq.add(s);
            while (!pq.isEmpty()) {
                Node top = pq.pollFirst();
                for (Edge e : top.adj) {
                    Node node = e.other(top);
                    long newDist = top.dists[i] + e.len;
                    if (newDist < node.dists[i]) {
                        pq.remove(node);
                        node.ways[i] = 0;
                        node.dists[i] = newDist;
                        pq.add(node);
                    }
                    if (newDist == node.dists[i]) {
                        node.ways[i] = mod.plus(node.ways[i], top.ways[i]);
                    }
                }
            }
        }

    }

    static class Modular {
        int m;

        public Modular(int m) {
            this.m = m;
        }

        public Modular(long m) {
            this.m = (int) m;
            if (this.m != m) {
                throw new IllegalArgumentException();
            }
        }

        public Modular(double m) {
            this.m = (int) m;
            if (this.m != m) {
                throw new IllegalArgumentException();
            }
        }

        public int valueOf(int x) {
            x %= m;
            if (x < 0) {
                x += m;
            }
            return x;
        }

        public int valueOf(long x) {
            x %= m;
            if (x < 0) {
                x += m;
            }
            return (int) x;
        }

        public int mul(int x, int y) {
            return valueOf((long) x * y);
        }

        public int plus(int x, int y) {
            return valueOf(x + y);
        }

        public int subtract(int x, int y) {
            return valueOf(x - y);
        }

        public String toString() {
            return "mod " + m;
        }

    }

    static class Debug {
        private boolean offline;
        private PrintStream out = System.err;

        public Debug(boolean enable) {
            offline = enable && System.getSecurityManager() == null;
        }

        public Debug debug(String name, int x) {
            if (offline) {
                debug(name, "" + x);
            }
            return this;
        }

        public Debug debug(String name, String x) {
            if (offline) {
                out.printf("%s=%s", name, x);
                out.println();
            }
            return this;
        }

    }

    static class Node {
        int id;
        List<Edge> adj = new ArrayList<>();
        long[] dists = new long[2];
        int[] ways = new int[2];

        public String toString() {
            return "" + (id + 1);
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput append(int c) {
            cache.append(c);
            return this;
        }

        public FastOutput println(int c) {
            return append(c).println();
        }

        public FastOutput println() {
            cache.append(System.lineSeparator());
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static class Edge {
        Node a;
        Node b;
        long len;

        public Node other(Node x) {
            return x == a ? b : a;
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }
}