Go: package main

import (
	"container/heap"
	"fmt"
	"runtime"
)

type Node struct {
	NowPosition          int
	DiscountTicketTCount int
	Amount               int
}

type PriorityQueueNode []*Node

func (pq PriorityQueueNode) Len() int {
	return len(pq)
}

func (pq PriorityQueueNode) Less(i, j int) bool {
	return pq[i].Amount < pq[j].Amount
}

func (pq PriorityQueueNode) Swap(i, j int) {
	pq[i], pq[j] = pq[j], pq[i]
}

func (pq *PriorityQueueNode) Push(node interface{}) {
	*pq = append(*pq, node.(*Node))
}

func (pq *PriorityQueueNode) Pop() interface{} {
	old := *pq
	n := len(old)
	item := old[n-1]
	*pq = old[0 : n-1]
	return item
}

type Point struct {
	NextPoint int
	Fee       int
}

type Memo struct {
	NowPoint             int
	DiscountTicketTCount int
}

func main() {
	var c, n, m, s, d int
	var a, b, f int

	for {
		fmt.Scan(&c, &n, &m, &s, &d)
		if c == 0 && n == 0 && m == 0 && s == 0 && d == 0 {
			break
		}
		s--
		d--
		pointMap := make([][]Point, n)
		for i := 0; i < n; i++ {
			pointMap[i] = make([]Point, 0, n)
		}
		for i := 0; i < m; i++ {
			fmt.Scan(&a, &b, &f)
			a--
			b--
			pointMap[a] = append(pointMap[a], Point{NextPoint: b, Fee: f})
			pointMap[b] = append(pointMap[b], Point{NextPoint: a, Fee: f})
		}
		pq := make(PriorityQueueNode, 0, m)
		start := Node{NowPosition: s, DiscountTicketTCount: c, Amount: 0}
		heap.Push(&pq, &start)
		memo := make(map[Memo]int)
		for len(pq) != 0 {
			now := heap.Pop(&pq).(*Node)
			if now.NowPosition == d {
				fmt.Println(now.Amount)
				break
			}
			memo[Memo{NowPoint: now.NowPosition, DiscountTicketTCount: now.DiscountTicketTCount}] = now.Amount
			for _, v := range pointMap[now.NowPosition] {
				next := &Node{v.NextPoint, now.DiscountTicketTCount, now.Amount + v.Fee}
				if memoAmount, ok := memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}]; !ok || (ok && memoAmount > next.Amount) {
					memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}] = next.Amount
					heap.Push(&pq, next)
				}
				if now.DiscountTicketTCount > 0 {
					next = &Node{v.NextPoint, now.DiscountTicketTCount - 1, now.Amount + v.Fee/2}
					if memoAmount, ok := memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}]; !ok || (ok && memoAmount > next.Amount) {
						memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}] = next.Amount
						heap.Push(&pq, next)
					}
				}
			}
		}
		runtime.GC()
	}
}

C++: #include <iostream>
#include <cstdio>
#include <iomanip>
#include <vector>
#include <map>
#include <set>
#include <queue>
#include <bitset>
#include <stack>
#include <utility>
#include <numeric>
#include <algorithm>
#include <functional>
#include <cctype>
#include <complex>
#include <string>
#include <sstream>
#include <fstream>
#include <cassert>
using namespace std;

//common

typedef int  i32;
typedef long long i64,ll;
typedef long double ld;

#define BR "\n"
#define ALL(c) (c).begin(),(c).end()
#define REP(i,n) for(int i=0;i<(int)(n);++i)
#define FOR(i,l,r) for(int i=(int)l;i<(int)(r);++i)
#define EACH(it,o) for(auto it = (o).begin(); it != (o).end(); ++it)
#define IN(l,v,r) ((l)<=(v) && (v)<(r))

//config
//#define NDEBUG
//#define INF 1<<30
//#define EPS 1e-8
//const ll MOD =100000007;

//debug
#ifdef NDEBUG
#define DUMP(x)
#define DUMPLN(x)
#define DEBUG(x)
#define DEBUGLN(x)
#define LINE()
#define LINELN()
#define CHECK(exp,act)
#define STOP(e)
#else
#define DUMP(x)  cerr << #x << " = " << (x)
#define DUMPLN(x)  DUMP(x) <<endl
#define DEBUG(x) DUMP(x) << LINE() << " " << __FILE__
#define DEBUGLN(x) DEBUG(x)<<endl
#define LINE()    cerr<< " (L" << __LINE__ << ")"
#define LINELN()    LINE()<<endl
#define CHECK(exp,act)  if(exp!=act){DUMPLN(exp);DEBUGLN(act);}
#define STOP(e)  CHECK(e,true);if(!(e)) exit(1);
#endif

template<class T> inline string toString(const vector<T>& x) {
	stringstream ss;
	REP(i,x.size()){
		if(i!=0)ss<<" ";
		ss<< x[i];
	}
	return ss.str();
}

template<class T> inline string toString(const vector<vector<T> >& map) {
	stringstream ss;
	REP(i,map.size()){
		if(i!=0)ss<<BR;
		ss<< toString(map[i]);
	}
	return ss.str();
}
template<class K,class V>  string toString(map<K,V>& x) {
	string res;stringstream ss;
	for(auto& p:x)ss<< p.first<<":" << p.second<<" ";
	return ss.str();
}

string BITtoString(int bit){
    stringstream ss;
    while(bit!=0){ss<<(bit%2);bit/=2;}
    string res=ss.str();reverse(ALL(res));
    return res;
}

template<typename T,typename V> inline T pmod(T v,V MOD){
	return (v%MOD+MOD)%MOD;
}
#define nextInt(n) scanf("%d",&n)
#define defInt(n) int n;nextInt(n)
#define nextLong(n) scanf("%lld",&n)
#define defLong(n) ll n;nextLong(n)
#define nextDouble(n) scanf("%lf",&n)

namespace ShortestPath{
    typedef ll Cost;
    const Cost CINF=1LL<<58;
    typedef  vector<vector<Cost> > Mat;
    struct Edge{
        int from,to;Cost cost;
        Edge(int from,int to,Cost cost)
            : from(from),to(to),cost(cost) {};
    };
    ostream& operator <<(ostream& os,const Edge& e){
            os<<"("<<e.from<<"->"<<e.to<<")";
            return os;
    }
    typedef vector<vector<Edge> > Graph;

    struct Task{
        int prev,pos;Cost cost;int c;
        Task(int prev,int pos,Cost cost,int c)
            :prev(prev),pos(pos),cost(cost),c(c){};
        bool operator>(const Task& r) const{
            return cost>r.cost;
        }
    };
 
    //verified by codoforces 144D http://codeforces.com/contest/144/submission/4976825
    // // 負の辺がない
    // // O(E*logV)
    vector<vector<Cost> > dijkstra(const Graph& g,const int s,const int c,vector<int>& prev){
        const int V=g.size();
        vector<vector<Cost> > d(V,vector<Cost>(c+1,CINF));
        d[s][c]=0;
        fill(ALL(prev), -2);
        priority_queue<Task,vector<Task>,greater<Task> > que;
        que.push(Task(-1,s,0,c));
        while(!que.empty()){
            Task task=que.top();que.pop();
            //if(prev[task.pos]!=-2)continue;
            if(d[task.pos][task.c]<task.cost)continue;
            prev[task.pos]=task.prev;
            EACH(e,g[task.pos]){
                if(d[e->to][task.c]>d[e->from][task.c]+e->cost){
                    d[e->to][task.c]=d[e->from][task.c]+e->cost;
                    que.push(Task(e->from,e->to,d[e->to][task.c],c));
                }
                if(task.c>0 && d[e->to][task.c-1]>d[e->from][task.c]+e->cost/2){
                    d[e->to][task.c-1]=d[e->from][task.c]+e->cost/2;
                    que.push(Task(e->from,e->to,d[e->to][task.c-1],c-1));
                }
            }   
        }
        return d;
    }
    vector<vector<Cost> > dijkstra(const Graph& g,const int s,const int c){
        vector<int> prev(g.size());return dijkstra(g,s,c,prev);
    }
}
using namespace ShortestPath;

class Main{
public:
	void run(){
	//	ifstream cin("in");
	//	ofstream cout( "out" );
		while(true){
			int C,N,M,S,D;nextInt(C);nextInt(N);nextInt(M);nextInt(S);nextInt(D);
			S--;D--;
			if(N==0 && M==0)break;
				
			Graph g(N);
			REP(i,M){
				int f,t,c;nextInt(f);nextInt(t);nextInt(c);f--;t--;
				g[f].push_back(Edge(f,t,c));
				g[t].push_back(Edge(t,f,c));
			}
			vector<vector<Cost>> res=dijkstra(g,S,C);

			Cost mv=CINF;
			REP(c,C+1) mv=min(mv,res[D][c]);

			cout <<mv <<endl;
		}
	}
};
int main(){
	cout <<fixed<<setprecision(13);	
	ios::sync_with_stdio(false);
	Main().run();
	return 0;
}