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 <vector>
#include <queue>
#include <map>
#include <cassert>
#include <algorithm>
using namespace std;
typedef pair<int, int> edge;
struct state{
  int cost, coupon, station;
  state(int cost_, int coupon_, int station_):cost(cost_), coupon(coupon_), station(station_){}
  bool operator< (const state &s) const{
    if(cost == s.cost){
      return coupon > s.coupon;
    }
    return cost > s.cost;
  }
};
int djikstra(vector<vector<edge> > graph, int start, int goal, int coupon){
  priority_queue<state> pq;
  pq.push(state(0, coupon, start));
  bool visited[coupon][graph.size()];
  return 0;
  fill_n((bool*)visited, (coupon+1) * graph.size(), false);
  while(!pq.empty()){
    state cur = pq.top(); pq.pop();
    if(visited[cur.coupon][cur.station]){
      continue;
    }
    if(cur.station == goal){
      return cur.cost;
    }
    visited[cur.coupon][cur.station] = true;
    for(int i = 0; i < graph[cur.station].size(); ++i){
      int to = graph[cur.station][i].first;
      int c = graph[cur.station][i].second;
      if(cur.coupon > 0){
        pq.push(state(cur.cost+c/2, cur.coupon-1, to));
      }
      pq.push(state(cur.cost+c, cur.coupon, to));
    }
  }
  //assert(false);
  return -1;
}
int main(){
  int c, n, m, s, d;
  while(true){    
    cin >> c >> n >> m >> s >> d;
    if((c|n|m|s|d) == 0){
      break;
    }
    vector<vector<edge> > graph(n+1, vector<edge>());
    for(int i = 0; i < m; ++i){
      int a, b, f;
      cin >> a >> b >> f;
      graph[a].push_back(make_pair(b, f));
      graph[b].push_back(make_pair(a, f));
    }
    cout << djikstra(graph, s, d, c) << endl;
  }
  return 0;
}

C++: #include <vector>
#include <map>
#include <set>
#include <stack>
#include <queue>
#include <algorithm>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <string>
#include <cstring>
#include <complex>
#include <ctime>
#include <cstdlib>

using namespace std;
const int INF = 1 << 30;
int main()
{
	int wk, tk, c;
	int disc, city, line, start, goal;
	int route[512][512], cost[512][16];
	bool used[512];
	while(cin >> disc >> city >> line >> start >> goal)
	{
		if(!disc && !city && !line && !start && !goal) break;

		start--, goal--;
		for(int i = 0; i < city; i++)
		{
			fill(route[i], route[i] + city, INF);
			fill(cost[i], cost[i] + city, INF);
		}

		for(int i = 0; i < line; i++)
		{
			cin >> wk >> tk >> c;
			route[wk-1][tk-1] = c;
			route[tk-1][wk-1] = c;
		}

		for(int m = 0; m <= disc; m++)
		{
			cost[start][m] = 0;
			fill(used, used + city, false);

			while(true)
			{
				int v = -1;
				for(int i = 0; i < city; i++)
				{
					if(!used[i] && (v == -1 || cost[i][m] < cost[v][m])) v = i;
				}

				if(v == -1) break;

				used[v] = true;

				for(int i = 0; i < city; i++)
				{
					if(m == 0)
					{
						cost[i][m] = min(cost[i][m], cost[v][m] + route[v][i]);
					}
					else
					{
						cost[i][m] = min(cost[v][m - 1] + route[v][i] / 2, min(cost[i][m], cost[v][m] + route[v][i]));
					}
				}
			}
		}
		cout <<	cost[goal][disc] << endl;
	}
}

C++: //Solution for aoj:0212 Highway Express Bus
#include<iostream>
#include<algorithm>
#include<vector>
#include<queue>
#include<functional>
using namespace std;
typedef pair<int, int>P;


struct S {
	int cost, to, num;
	S(int c, int t, int n) : cost(c), to(t), num(n){}
	bool operator>(const S &s) const {
		return cost > s.cost;
	}
};

const int INF = 1 << 30;
int c, n, m, s, d, ans;
int tocost[1010][110];
vector<P> town[5001];
priority_queue<S, vector<S>, greater<S> > pq;


void dijkstra(){
	while (!pq.empty()){
		S a = pq.top();
		pq.pop();
		for (int i = 0; i < town[a.to].size(); i++){
			int tt = town[a.to][i].first, cc = town[a.to][i].second;
			if (tocost[tt][a.num] > cc + a.cost){
				tocost[tt][a.num] = cc + a.cost;
				pq.push({ cc + a.cost, tt, a.num });
			}
			if (a.num&&tocost[tt][a.num-1] > cc/2 + a.cost){
				tocost[tt][a.num-1] = cc/2 + a.cost;
				pq.push({ cc/2 + a.cost, tt, a.num-1 });
			}
		}
	}
}
	int main(){
		while (cin >> c >> n >> m >> s >> d&&c){
			for (int i = 0; i < 101; i++)
				fill(tocost[i], tocost[i] + 110, INF);
			tocost[s][c] = 0;
			ans = INF;
			while (pq.size())
				pq.pop();
			for (int i = 0; i < n; i++)
					town[i].erase(town[i].begin(),town[i].end());
			for (int i = 0; i < m; i++){
				int a, b, c;
				cin >> a >> b >> c;
				town[a].push_back({ b, c });
				town[b].push_back({ a, c });
			}
			pq.push({ 0, s, c });
			dijkstra();
			for (int i = 0; i <= c; i++)
				ans = min(ans, tocost[d][i]);
			cout << ans << endl;
		}
		return 0;
	}