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<queue>
#include<vector>

using namespace std;

#define REP(i, n) for(int i=0; i<n; i++)

struct edge{
    int to, cost;
};

typedef pair<int, pair<int, int> > pii; // distance, edge, ticket

int INF = 10e8;
int c, n, m, s, d;

int dis[100][11];

int main(){
    while(1){
        cin >> c >> n >> m >> s >> d;

        if(n==0) break;

        vector<edge> g[100];
        REP(i, m){
            int a, b, f;
            cin >> a >> b >> f;
            edge ae;
            ae.to = b;
            ae.cost = f;
            g[a].push_back(ae);
            edge be;
            be.to = a;
            be.cost = f;
            g[b].push_back(be);
        }

        priority_queue<pii, vector<pii>, greater<pii> > que;
        REP(i, n+1){
            REP(j, c+1){
                dis[i][j] = INF;
            }
        }
        dis[s][c] = 0;
        pii init = make_pair(0, make_pair(s, c));
        que.push(init);

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

            int v = p.second.first;
            int t = p.second.second;
            if(dis[v][t]<p.first) continue;
            REP(i, g[v].size()){
                edge e = g[v][i];
                if(dis[e.to][t] > dis[v][t] + e.cost){
                    dis[e.to][t] = dis[v][t] + e.cost;
                    que.push(pii(make_pair(dis[e.to][t], make_pair(e.to, t))));
                }
                if(t>0){
                    if(dis[e.to][t-1] > dis[v][t] + e.cost / 2){
                        dis[e.to][t-1] = dis[v][t] + e.cost / 2;
                        que.push(pii(make_pair(dis[e.to][t-1], make_pair(e.to, t-1))));
                    }
                }
            }
        }
        /*
        REP(i, n+1){
            REP(j, c+1){
                cout << dis[i][j] << " ";
            }
            cout << endl;
        }
        */
        cout << dis[d][0] << endl;
    }
}

C++: #include <iostream>
#include <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <queue>
#include <stack>
#include <algorithm>

using namespace std;

#define rep(i,j) REP((i), 0, (j))
#define REP(i,j,k) for(int i=(j);(i)<(k);++i)
#define BW(a,x,b) ((a)<=(x)&&(x)<=(b))
#define ALL(v) (v).begin(), (v).end()
#define LENGTHOF(x) (sizeof(x) / sizeof(*(x)))
#define AFILL(a, b) fill((int*)a, (int*)(a + LENGTHOF(a)), b)
#define MP make_pair
#define PB push_back
#define F first
#define S second
#define INF 1 << 30
#define EPS 1e-10

typedef pair<int, int> pi; // 残りの割引券 現在の街
typedef pair<int, pi>P; // コスト pi
typedef vector<int> vi;
typedef queue<int> qi;
typedef long long ll;

struct edge{ int to, cost; };

int C, V, E, S, D;
int d[128][16];
vector<vector<edge> >G(100);

void dijkstra(int s){
  priority_queue<P, vector<P>, greater<P> >q;
  rep(i, V) rep(j, C) d[i][j] = INF;
  d[s][C] = 0;
  q.push(MP(0, MP(C, s)));

  while(!q.empty()){
    P p = q.top(); q.pop();
    int v = p.S.S;
    int c = p.S.F;

    rep(i, G[v].size()){
      edge e = G[v][i];
      if(d[e.to][c] > d[v][c] + e.cost){
	d[e.to][c] = d[v][c] + e.cost;
	q.push(MP(d[e.to][c], MP(c, e.to)));
      }

      if(C > 0){
	//	int cost = (e.cost/2)/100*100;
	if(d[e.to][c-1] > d[v][c] + e.cost/2){
	  d[e.to][c-1] = d[v][c] + e.cost/2;
	  q.push(MP(d[e.to][c-1], MP(c-1, e.to)));
	}
      }
    }
  }
}

int main(){
  while(scanf("%d%d%d%d%d", &C, &V, &E, &S, &D) && C+V+E+S+D){
    S--; D--;
    rep(i, V){
      G[i].clear();
    }
    rep(i, E){
      int a, b, c;
      scanf("%d%d%d", &a, &b, &c); a--; b--;
      edge e;
      e.to = a; e.cost = c;
      G[b].PB(e);
      e.to = b;
      G[a].PB(e);
    }

    dijkstra(S);

    printf("%d\n", d[D][0]);
  }

  return 0;
}

C++: #include<iostream>
#include<queue>
#include<vector>
#include<algorithm>
using namespace std;
#define INF (1<<24)
 
struct state{
  int cost,pos,cnt;
  bool operator < (const state &p) const{
    return cost>p.cost;
  }
};
 
struct edge{
  int to,cost;
};
 
int c,n,m,s,d;
vector<edge> G[100];
 
void init(){
  for(int i=0;i<100;i++)G[i].clear();
}
 
int dijkstra(int si,int ti){
  int d[100][11];
  for(int i=0;i<100;i++)
    for(int j=0;j<11;j++)d[i][j]=INF;
 
  d[si][c]=0;
  priority_queue< state > Q;
  Q.push((state){0,si,c});
 
  while(!Q.empty()){
    state s=Q.top();Q.pop();
    if(s.cost>d[s.pos][s.cnt])continue;
 
    for(int i=0;i<(int)G[s.pos].size();i++){
      edge e=G[s.pos][i];
      if(s.cost+e.cost>=d[e.to][s.cnt])continue;
      d[e.to][s.cnt]=s.cost+e.cost;
      Q.push((state){s.cost+e.cost,e.to,s.cnt});
    }
 
    if(s.cnt==0)continue;
 
    for(int i=0;i<(int)G[s.pos].size();i++){
      edge e=G[s.pos][i];
      if(s.cost+e.cost/2>=d[e.to][s.cnt-1])continue;
      d[e.to][s.cnt-1]=s.cost+e.cost/2;
      Q.push((state){s.cost+e.cost/2,e.to,s.cnt-1});
    }
  }//while
 
  int res=INF;
  for(int i=0;i<=c;i++){
    res=min(res,d[ti][i]);
  }
  return res;
}
 
int main(){
  int a,b,f;
  while(cin>>c>>n>>m>>s>>d){
    if(n==0)break;
    init();
    for(int i=0;i<m;i++){
      cin>>a>>b>>f;
      a--;b--;
      G[a].push_back((edge){b,f});
      G[b].push_back((edge){a,f});
    }
    cout<<dijkstra(s-1,d-1)<<endl;
  }
  return 0;
}