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, 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<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<<29;

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<algorithm>
#include<queue>

using namespace std;

typedef pair<int,pair<int,int> >P;

struct Edge{
  int to,cost;
  Edge(int _to, int _cost):to(_to), cost(_cost){};
};

int minCost[101][11];
vector<Edge> edge[101];
static const int INF = INT_MAX;

int c,n,m,s,d;

int dijkstra(void){
  priority_queue<P, vector<P>, greater<P> >que;
  que.push(make_pair(0,make_pair(s,c)));

  for(int i=0;i<=n;i++)
    for(int j=0;j<=n;j++)
      minCost[i][j]=INF;

  while(!que.empty()){
    P p = que.top();
    que.pop();

    if(p.second.first==d)return p.first;

    for(int i=0;i<edge[p.second.first].size();i++){
      Edge e = edge[p.second.first][i];
      que.push(make_pair(p.first+e.cost,make_pair(e.to,p.second.second)));
    }
    if(p.second.second==0)continue;
    
    for(int j=0;j<edge[p.second.first].size();j++){
      Edge e = edge[p.second.first][j];
      que.push(make_pair(p.first+e.cost/2,make_pair(e.to,p.second.second-1)));
    }
  }
  return -1;
}

int main(void){
  int a,b,f;

  while(cin >> c >> n >> m >> s >> d,c|n|m|s|d){

    for(int i=0;i<=n;i++)edge[i].clear();

    for(int i=0;i<m;i++){
      cin >> a >> b >> f;
      edge[a].push_back(Edge(b,f));
      edge[b].push_back(Edge(a,f));
    }

    cout << dijkstra() << endl;
  }

  return 0;
}

C++: #include <cstdio>
#include <cstdlib>
#include <cmath>
#include <climits>
#include <cfloat>
#include <map>
#include <utility>
#include <ctime>
#include <set>
#include <iostream>
#include <memory>
#include <string>
#include <cstring>
#include <vector>
#include <algorithm>
#include <functional>
#include <fstream>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
#include <cstring>
#include <numeric>
#include <cassert>
using namespace std;
#define rep(i, n) for (int(i) = 0; (i) < (n); (i)++)
class Timer
{
  private:
    double time_limit;
    //unsigned long long int cycle_per_sec = 2500000000; // Topcoder
    unsigned long long int cycle_per_sec = 2777777777; // AtCoder
    unsigned long long int beginCycle;
    unsigned long long int getCycle()
    {
        unsigned int low, high;
        __asm__ volatile("rdtsc"
                         : "=a"(low), "=d"(high));
        return ((unsigned long long int)low) | ((unsigned long long int)high << 32);
    }

  public:
    Timer(double time_limit) : time_limit(time_limit)
    {
        beginCycle = getCycle();
    }

    double elapsedTime()
    {

        return (double)(getCycle() - beginCycle) / cycle_per_sec;
    }
    bool isTLE()
    {
        return elapsedTime() >= time_limit;
    }
};

Timer gtimer(2.85);

struct NODE
{
    int to, cost, ticket;
    NODE(int to, int cost, int ticket) : to(to), cost(cost), ticket(ticket) {}
};
bool operator<(const NODE &a, const NODE &b)
{
    return a.cost > b.cost;
}
int main()
{
    int c, n, m, s, d;
    while (cin >> c >> n >> m >> s >> d && c)
    {
        vector<NODE> g[110];

        for (int i = 0; i < m; i++)
        {
            int a, b, f;
            cin >> a >> b >> f;
            --a, --b;
            g[a].push_back(NODE(b, f, 0));
            g[b].push_back(NODE(a, f, 0));
            g[a].push_back(NODE(b, f / 2, 1));
            g[b].push_back(NODE(a, f / 2, 1));
        }
        --s, --d;
        priority_queue<NODE> Q;
        Q.push(NODE(s, 0, c));
        int done[110][11] = {};
        while (Q.size())
        {
            auto q = Q.top();
            Q.pop();
            if (q.ticket < 0)
                continue;
            if (done[q.to][q.ticket]++)
                continue;
            if (q.to == d)
            {
                cout << q.cost << endl;
                break;
            }
            for (auto e : g[q.to])
            {
                Q.push(NODE(e.to, q.cost + e.cost, q.ticket - e.ticket));
            }
        }
    }

    std::cout.flush();
    return 0;
}