using static System.Math;
using System.Collections.Generic;
using System;

public class PriorityQueue<T> where T : IComparable
{
    private IComparer<T> _comparer = null;
    private int _type = 0;
    private T[] _heap;
    private int _sz = 0;
    private int _count = 0;
    /// <summary>
    /// Priority Queue with custom comparer
    /// </summary>
    public PriorityQueue(int maxSize, IComparer<T> comparer)
    {
        _heap = new T[maxSize];
        _comparer = comparer;
    }

    /// <summary>
    /// Priority queue
    /// </summary>
    /// <param name="maxSize">max size</param>
    /// <param name="type">0: asc, 1:desc</param>
    public PriorityQueue(int maxSize, int type = 0)
    {
        _heap = new T[maxSize];
        _type = type;
    }
    private int Compare(T x, T y)
    {
        if (_comparer != null) return _comparer.Compare(x, y);
        return _type == 0 ? x.CompareTo(y) : y.CompareTo(x);
    }
    public void Push(T x)
    {
        _count++;
        //node number
        var i = _sz++;
        while (i > 0)
        {
            //parent node number
            var p = (i - 1) / 2;

            if (Compare(_heap[p], x) <= 0) break;

            _heap[i] = _heap[p];
            i = p;
        }
        _heap[i] = x;
    }
    public T Pop()
    {
        _count--;
        T ret = _heap[0];
        T x = _heap[--_sz];

        int i = 0;
        while (i * 2 + 1 < _sz)
        {
            //children
            int a = i * 2 + 1;
            int b = i * 2 + 2;

            if (b < _sz && Compare(_heap[b], _heap[a]) < 0) a = b;

            if (Compare(_heap[a], x) >= 0) break;

            _heap[i] = _heap[a];
            i = a;
        }
        _heap[i] = x;
        return ret;
    }
    public int Count()
    {
        return _count;
    }
    public T Peek()
    {
        return _heap[0];
    }
    public bool Contains(T x)
    {
        for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true;
        return false;
    }
    public void Clear()
    {
        while (this.Count() > 0) this.Pop();
    }
    public IEnumerator<T> GetEnumerator()
    {
        var ret = new List<T>();
        while (this.Count() > 0)
        {
            ret.Add(this.Pop());
        }
        foreach (var r in ret)
        {
            this.Push(r);
            yield return r;
        }
    }
    public T[] ToArray()
    {
        T[] array = new T[_sz];
        int i = 0;
        foreach (var r in this)
        {
            array[i++] = r;
        }
        return array;
    }
}
public class Edge
{
    public int to { get; set; }
    public int ticket { get; set; }
    public long f { get; set; }
}
public class Node : IComparable
{
    public int id { get; set; }
    public int ticket { get; set; }
    public long f { get; set; }
    public int CompareTo(object obj)
    {
        var x = (Node)obj;
        if (this.f > x.f) return 1;
        else if (this.f == x.f) return 0;
        else return -1;
    }
}

public class hello
{
    public static void Main()
    {
        while (true)
        {
            string[] line = Console.ReadLine().Trim().Split(' ');
            var c = int.Parse(line[0]);
            var n = int.Parse(line[1]);
            var m = int.Parse(line[2]);
            var s = int.Parse(line[3]);
            var d = int.Parse(line[4]);
            if (c == 0 && n == 0 && m == 0 && s == 0 && d == 0) break;
            s--;  d--;
            var aa = getEdge(c, n, m);


            var mind = new long[n, c + 1];
            for (int i = 0; i < n; i++)
                for (int j = 0; j < c + 1; j++) mind[i, j] = 9999999999999;
            goDijk(aa, s,c , mind);
            putAns(mind, c, d);
        }
    }
    static void putAns (long[,] mind , int c, int d)
    {
        var ans = long.MaxValue;
        for (int i = 0; i < c + 1; i++)
            ans = Min(ans, mind[d, i]);
        Console.WriteLine(ans);
    }
    static List<Edge>[,] getEdge(int c, int n, int m)
    {
        var aa = new List<Edge>[n, c + 1];
        for (int i = 0; i < n; i++)
            for (int j = 0; j < c + 1; j++) aa[i, j] = new List<Edge>();
        for (int i = 0; i < m; i++)
        {
            string[] line = Console.ReadLine().Trim().Split(' ');
            var a = int.Parse(line[0]) - 1;
            var b = int.Parse(line[1]) - 1;
            var f = int.Parse(line[2]);
            for (int j = 1; j <= c; j++)
            {
                aa[a, j].Add(new Edge { to = b, ticket = j, f = f });
                aa[a, j].Add(new Edge { to = b, ticket = j - 1, f = f / 2 });
                aa[b, j].Add(new Edge { to = a, ticket = j, f = f });
                aa[b, j].Add(new Edge { to = a, ticket = j - 1, f = f / 2 });
            }
            aa[a, 0].Add(new Edge { to = b, ticket = 0, f = f });
            aa[b, 0].Add(new Edge { to = a, ticket = 0, f = f });
        }
        return aa;
    }
    public static void goDijk(List<Edge>[,] aa, int r0, int r1 ,  long[,] mind)
    {
        var pq = new PriorityQueue<Node>(100000);
        pq.Push(new Node { id = r0, ticket = r1, f = 0 });
        while (pq.Count() > 0)
        {
            var targ = pq.Pop();
            var nowd = targ.f;
            var nowid = targ.id;
            var nowid2 = targ.ticket;
            if (mind[nowid, nowid2] < nowd) continue;
            mind[nowid, nowid2] = nowd;
            foreach (var x in aa[nowid,nowid2])
                if (nowd + x.f < mind[x.to, x.ticket])
                {
                    mind[x.to, x.ticket] = nowd + x.f;
                    pq.Push(new Node { id = x.to, ticket = x.ticket, f = nowd + x.f });
                }

        }
    }
}



Measured memory_bytes: 35464