using System;
using System.Linq;
using System.Collections.Generic;
using System.Numerics;
using Debug = System.Diagnostics.Debug;
using SB = System.Text.StringBuilder;
using Number = System.Int64;
using static System.Math;
using ll = System.Int64;
namespace Program {
    public class Solver {
        Random rnd = new Random();
        public void Solve() {
            var n = ri;
            var m = ri;
            var s = ri - 1; var t = ri - 1;
            var G = Enumerate(n, x => new List<KeyValuePair<int, long>>());
            for (int i = 0; i < m; i++)
            {
                var u = ri - 1;
                var v = ri - 1;
                var d = ri;
                G[u].Add(new KeyValuePair<int, Number>(v, d));
                G[v].Add(new KeyValuePair<int, Number>(u, d));
            }
            long[] da, db;
            ModInt[] pa, pb;
            solve(n, s, G, out da, out pa);
            solve(n, t, G, out db, out pb);
            Debug.WriteLine(da.AsJoinedString());
            Debug.WriteLine(db.AsJoinedString());
            var all = pa[t] * pb[s];
            for (int i = 0; i < n; i++)
            {
                if (da[i] == db[i] && 2 * da[i] == da[t]) all -= pa[i] * pa[i] * pb[i] * pb[i];
                foreach (var e in G[i])
                {
                    var j = e.Key;
                    var dd = e.Value;
                    if (da[i] + dd != da[j]) continue;
                    if (db[j] + dd != db[i]) continue;
                    if (da[i] + db[j] + dd != da[t]) continue;
                    var A = da[i]; var B = da[i] + dd;
                    var C = db[j]; var D = db[j] + dd;
                    var ma = Max(A, C);
                    var mi = Min(B, D);
                    if (ma < mi)
                    {
                        all -= pa[i] * pa[i] * pb[j] * pb[j];
                    }

                }
            }
            Console.WriteLine(all);
        }

        void solve(int n, int src, List<KeyValuePair<int, long>>[] G, out long[] dist, out ModInt[] pat) {
            dist = Enumerate(n, x => 1L << 60);
            pat = new ModInt[n];

            dist[src] = 0;
            pat[src] = 1;
            var pq = new PriorityQueue<KeyValuePair<int, long>>((l, r) => l.Value.CompareTo(r.Value));
            pq.Enqueue(new KeyValuePair<int, Number>(src, 0));
            while (pq.Any())
            {
                var p = pq.Dequeue();
                var u = p.Key; var d = p.Value;
                foreach (var e in G[u])
                {
                    var v = e.Key;
                    var nd = d + e.Value;
                    if (nd < dist[v])
                    {
                        dist[v] = nd;
                        pat[v] = pat[u];
                        pq.Enqueue(new KeyValuePair<int, Number>(v, nd));
                    }
                    else if (nd == dist[v])
                        pat[v] += pat[u];
                }
            }

        }
        const long MOD = (long)1e9 + 7;
        const long INF = 1L << 60;
        //int[] dx = { -1, 0, 1, 0 };
        //int[] dy = { 0, 1, 0, -1 };

        int ri { get { return sc.Integer(); } }
        long rl { get { return sc.Long(); } }
        double rd { get { return sc.Double(); } }
        string rs { get { return sc.Scan(); } }
        public IO.StreamScanner sc = new IO.StreamScanner(Console.OpenStandardInput());

        static T[] Enumerate<T>(int n, Func<int, T> f) {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f(i);
            return a;
        }
        static public void Swap<T>(ref T a, ref T b) { var tmp = a; a = b; b = tmp; }
    }
}

#region main
static class Ex {
    static public string AsString(this IEnumerable<char> ie) { return new string(ie.ToArray()); }

    static public string AsJoinedString<T>(this IEnumerable<T> ie, string st = " ") {
        return string.Join(st, ie.Select(x => x.ToString()).ToArray());
        //return string.Join(st, ie);
    }

    static public void Main() {
        Console.SetOut(new Program.IO.Printer(Console.OpenStandardOutput()) { AutoFlush = false });
        var solver = new Program.Solver();
        solver.Solve();
        Console.Out.Flush();
    }
}
#endregion
#region Ex
namespace Program.IO {
    using System.IO;
    using System.Text;
    using System.Globalization;

    public class Printer: StreamWriter {
        public override IFormatProvider FormatProvider { get { return CultureInfo.InvariantCulture; } }
        public Printer(Stream stream) : base(stream, new UTF8Encoding(false, true)) { }
    }

    public class StreamScanner {
        public StreamScanner(Stream stream) { str = stream; }

        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;
        public bool IsEndOfStream { get { return isEof; } }

        private byte read() {
            if (isEof) return 0;
            if (ptr >= len)
            {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }

        public char Char() {
            byte b = 0;
            do b = read(); while ((b < 33 || 126 < b) && !isEof);
            return (char)b;
        }
        public string Scan() {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read()) sb.Append(b);
            return sb.ToString();
        }
        public string ScanLine() {
            var sb = new StringBuilder();
            for (var b = Char(); b != '\n' && b != 0; b = (char)read()) if (b != '\r') sb.Append(b);
            return sb.ToString();
        }
        public long Long() { return isEof ? long.MinValue : long.Parse(Scan()); }
        public int Integer() { return isEof ? int.MinValue : int.Parse(Scan()); }
        public double Double() { return isEof ? double.NaN : double.Parse(Scan(), CultureInfo.InvariantCulture); }
    }
}

#endregion

#region ModInt
public struct ModInt {
    public const long Mod = (long)1e9 + 7;
    public long num;
    public ModInt(long n) { num = n; }
    public override string ToString() { return num.ToString(); }
    public static ModInt operator +(ModInt l, ModInt r) { l.num += r.num; if (l.num >= Mod) l.num -= Mod; return l; }
    public static ModInt operator -(ModInt l, ModInt r) { l.num -= r.num; if (l.num < 0) l.num += Mod; return l; }
    public static ModInt operator *(ModInt l, ModInt r) { return new ModInt((int)(l.num * r.num % Mod)); }
    public static implicit operator ModInt(long n) { n %= Mod; if (n < 0) n += Mod; return new ModInt(n); }
    public static ModInt Pow(ModInt v, long k) { return Pow(v.num, k); }
    public static ModInt Pow(long v, long k) {
        long ret = 1;
        for (k %= Mod - 1; k > 0; k >>= 1, v = v * v % Mod)
            if ((k & 1) == 1) ret = ret * v % Mod;
        return new ModInt(ret);
    }
    public static ModInt Inverse(ModInt v) { return Pow(v, Mod - 2); }
}
#endregion


#region BinaryHeap
public class PriorityQueue<T> {
    readonly List<T> heap = new List<T>();
    readonly Comparison<T> compare;
    public PriorityQueue() { compare = Comparer<T>.Default.Compare; }

    public PriorityQueue(Comparison<T> comparison) { compare = comparison; }
    public PriorityQueue(IComparer<T> comparer) { compare = comparer.Compare; }

    public void Enqueue(T item) {
        var pos = heap.Count;
        heap.Add(item);
        while (pos > 0)
        {
            var par = (pos - 1) / 2;
            if (compare(heap[par], item) <= 0)
                break;
            heap[pos] = heap[par];
            pos = par;
        }
        heap[pos] = item;

    }

    public T Dequeue() {
        var ret = heap[0];
        var pos = 0;
        var x = heap[heap.Count - 1];

        while (pos * 2 + 1 < heap.Count - 1)
        {
            var lch = pos * 2 + 1;
            var rch = pos * 2 + 2;
            if (rch < heap.Count - 1 && compare(heap[rch], heap[lch]) < 0) lch = rch;
            if (compare(heap[lch], x) >= 0)
                break;
            heap[pos] = heap[lch];
            pos = lch;
        }
        heap[pos] = x;
        heap.RemoveAt(heap.Count - 1);
        return ret;

    }
    public T Peek() { return heap[0]; }
    public int Count { get { return heap.Count; } }
    public bool Any() { return heap.Count > 0; }

    public T[] Items {
        get {
            var ret = heap.ToArray();
            Array.Sort(ret, compare);
            return ret;
        }
    }
}
#endregion

Measured memory_bytes: 45576