Go: package main

import (
	"container/heap"
	"fmt"
)

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)
		}
		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)
		start := Node{NowPosition: s, DiscountTicketTCount: c, Amount: 0}
		heap.Push(&pq, &start)
		memo := make(map[Memo]struct{})
		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}] = struct{}{}
			for _, v := range pointMap[now.NowPosition] {
				next := &Node{v.NextPoint, now.DiscountTicketTCount, now.Amount + v.Fee}
				if _, ok := memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}]; !ok {
					heap.Push(&pq, next)
				}
				if now.DiscountTicketTCount > 0 {
					next = &Node{v.NextPoint, now.DiscountTicketTCount - 1, now.Amount + v.Fee/2}
					if _, ok := memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}]; !ok {
						heap.Push(&pq, next)
					}
				}
			}
		}
	}
}

C++: #include<iostream>
#include<algorithm>
#include<queue>
#include<vector>
#define REP(i,s,n) for(int i=s;i<n;i++)
#define rep(i,n) REP(i,0,n)
#define F first
#define S second
using namespace std;
typedef pair<int,int> P;// F -> to, S -> cost
typedef pair<P,int> PP;// F->P(to,cost), S->discount
int c,n,m,s,d;
vector<P> vec[1000]; // F -> pos , S -> cost
int MD[1000][13];
const int INF = 1<<27;

//C++だとなぜかRuntimeErrorになったので仕様変更
//vecにはコストいらないからvector<PP> vec -> vector<P> vec へ


void dijkstra(){
  priority_queue<PP,vector<PP>,greater<PP> > que;
  rep(i,n+1)rep(j,13)MD[i][j] = INF;
  //syokika
  MD[s][c] = 0;
  que.push(PP(P(0,s),c));//dis,start,discount

  while(!que.empty() ){
    PP p = que.top();que.pop(); //priority_queのPPと
    int v = p.F.S;
    
    for(int i=0;i<vec[v].size();i++){
      P po = vec[v][i]; //vectorのPPは意味が違うので注意！！！
      //if(MD[v][po.S] < po.F.S)continue;
      if(MD[po.F][p.S] > p.F.F + po.S){
	MD[po.F][p.S] = p.F.F+po.S;
	que.push(PP(P(MD[po.F][p.S],po.F),p.S));
      }
      if(p.S > 0 && MD[po.F][p.S-1] > p.F.F + po.S/2 ){
	MD[po.F][p.S-1] = p.F.F+po.S/2;
	que.push(PP(P(MD[po.F][p.S-1],po.F),p.S-1));
   
      }
    }
  }
}


int main(){
  int x,y,co;
  while(true){
    cin >> c >> n >> m >> s >> d;
    if(c+n+m+s+d == 0)break;
    rep(i,1000)vec[i].clear();
    rep(i,m){
      cin >> x >> y >> co;
      vec[x].push_back(P(y,co));
      vec[y].push_back(P(x,co));
    }
    dijkstra();
    int ans = INF;
    for(int i=0;i<=c;i++){
      ans = min(ans,MD[d][i]);
    }
    cout << ans << endl;
  }
  return 0;
}

//Version.1

C++: #include <iostream>
#include <vector>
#include <queue>
#include <utility>
using namespace std;

int calcCost(int c, int n, vector<int> path, vector<int> rt){
	priority_queue<int> costs;
	for(int i=1; i<rt.size(); i++){
		costs.push(path[rt[i]+n*rt[i-1]]);
	}
	int total = 0;
	while(costs.size() && c--){
		total += costs.top() / 2;
		costs.pop();
	}
	while(costs.size()){
		total += costs.top();
		costs.pop();
	}
	return total;
}
int main(){
	for(;;){
		int c,n,m,s,d;
		cin>>c>>n>>m>>s>>d;
		if(c+n+m+s+d==0) break;
		vector<pair<int, vector<int>>> route(n,make_pair(-1,vector<int>()));
		vector<int> path(n*n,-1);
		for(int i=0; i<m; i++){
			int a,b,f;
			cin>>a>>b>>f;
			path[--a+n*--b] = path[b+n*a] = f;
		}
		priority_queue<pair<int, vector<int>>, vector<pair<int, vector<int>>>, greater<pair<int, vector<int>>>> pq;
		pq.push(make_pair(0,vector<int>(1,s-1)));
		while(pq.size()){
			int cur = *(pq.top().second.rbegin());
			if(route[cur].first == -1){
				route[cur] = pq.top();
				for(int i=0; i<m; i++){
					if(route[i].first == -1 && path[i+n*cur] != -1){
						pair<int, vector<int>> copy = pq.top();
						copy.second.push_back(i);
						copy.first = calcCost(c,n,path,copy.second);
						pq.push(copy);
					}
				}
			}
			pq.pop();
		}
		cout<<route[d-1].first<<endl;
	}
}

C++: /*
g£_CNXg
*/
#include<iostream>
#include<queue>
#include<map>
#define INF 10000000
#include<vector>
#define rep(i,n) for(int i=0;i<n;i++)
using namespace std;
typedef pair<int,int> p;
typedef pair<int,p> P;
//P(cost,p(node,ticket))
struct edge{
	int cost,to;
};
int nticket,nnode,nedge,start,goal,d[11][101];
vector<edge> v[101];
void dijkstra(){
	int nowticket,nowplace,nowsum;
	priority_queue<P,vector<P>,greater<P> > que;
	que.push(P(0,p(start,nticket)));
	while(!que.empty()){
		P now=que.top();
		que.pop();
		
		nowsum=now.first;
		nowplace=now.second.first;
		nowticket=now.second.second;
		
		if(d[nowticket][nowplace]<nowsum)
			continue;
		rep(i,(int)v[nowplace].size()){
			edge e=v[nowplace][i];
			if(nowticket>0){
				if(d[nowticket-1][e.to]>e.cost/2+nowsum){
				d[nowticket-1][e.to]=e.cost/2+nowsum;
				que.push(P(d[nowticket-1][e.to],p(e.to,nowticket-1)));
				}
			}
			if(d[nowticket][e.to]>e.cost+nowsum){
				d[nowticket][e.to]=e.cost+nowsum;
				que.push(P(d[nowticket][e.to],p(e.to,nowticket)));
			}
		}
	}
}
void input(){
	int a,b,f;
	rep(i,nedge){
			cin>>a>>b>>f;
			a--;b--;
			edge c;
			c.cost=f;
			c.to=b;v[a].push_back(c);
			c.to=a;v[b].push_back(c);
		}
}
void init(){
	rep(i,nticket+1)
		rep(j,nnode){
			if(j==start)
			d[i][j]=0;
			else
			d[i][j]=INF;
	}
}
int main(){
	//d[ticket][node]=Å­ïp
	while(cin>>nticket>>nnode>>nedge>>start>>goal,nticket||nnode||nedge||start||goal){
		start--;goal--;
		//ticket:`Pbg
		//nnode:nodeÌ
		//nedge:edgeÌ
		//start¨goal
		input();
		init();
		dijkstra();
		int ans=INF;
		for(int i=0;i<nticket+1;i++)
		if(ans>d[i][goal])
		ans=d[i][goal];
		cout<<ans<<endl;
		for(int i=0;i<nedge;i++)
		v[i].clear();
	}
	return 0;
}