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()];
  fill_n((bool*)visited, (coupon+1) * graph.size(), false);
  return 0;
  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 <iostream>
#include <queue>
#include <vector>
#include <cstdio>

#define reep(i,n,m) for(int i=(n);i<(m);i++)
#define rep(i,n) reep(i,0,n)

using namespace std;

class Edge{
public:
    int to;
    int cost;
    Edge(int to,int cost):to(to),cost(cost){}
};

class Node{
public:
    int distance;
    int num;
    int ticket;
    Node(){}
    Node(int distance, int num,int ticket):distance(distance),num(num),ticket(ticket){}
    bool operator<(const Node &b)const{
        return distance > b.distance;
    }
};

vector<Edge> edge[101];
bool flg[101][11];

int c,n,m,s,d;

int solve(){

    priority_queue<Node> Q;
    Q.push(Node(0,s,0));
    int ans = 1000000;
    while(!Q.empty()){
        Node node = Q.top();Q.pop();
        if(flg[node.num][node.ticket]){
            continue;
        }
        flg[node.num][node.ticket] = true;
        //printf("num->%d cost->%d ticket->%d\n",node.num,node.distance,node.ticket);
        if(node.num == d){
            ans = min(ans,node.distance);
        }

        rep(i,edge[node.num].size()){
            Edge e = edge[node.num][i];
            int cost = node.distance + e.cost;
            Q.push(Node(cost,e.to,node.ticket));
            if(node.ticket < c){
                int cost = node.distance + e.cost/2;
                Q.push(Node(cost,e.to,node.ticket+1));
            }
        }
    }
    return ans;
}



void init(){
    rep(i,101){
        edge[i].clear();
        rep(k,11){
            flg[i][k] = 0;
        }
    }
}

int main(){

    while(cin >> c >> n >> m >> s >> d,!m==0){
        init();
        rep(i,m){
            int a,b,c;
            cin >> a >> b >> c;
            edge[a].push_back(Edge(b,c));
            edge[b].push_back(Edge(a,c));
        }
        cout << solve() << endl;
    }
}

C++: #include <iostream>
#include <vector>

using namespace std;

#define INF 100000000

struct edge {
	int to, cost;
};

int main() {
	int c, n, m, s, d;
	while (cin >> c >> n >> m >> s >> d) {
		if (c == 0 && n == 0 && m == 0 && s == 0 && d == 0) {
			break;
		}
		//vector< vector<int> > ff(n+1, vector<int>(n+1, INF));
		vector<edge> ff[101];
		vector< vector<int> > ddd(n+1, vector<int>(n+1, INF));
		int a, b, f;
		for (int i = 0; i < m; i++) {
			cin >> a >> b >> f;
			edge e;
			e.to = b;
			e.cost = f;
			ff[a].push_back(e);
			e.to = a;
			ff[b].push_back(e);
			//ff[a][b] = ff[b][a] = f;
			ddd[a][b] = ddd[b][a] = f;
		}
		for (int i = 1; i <= n; i++) {
			ddd[i][i] = 0;
		}
		for (int k = 1; k <= n; k++) {
			for (int i = 1; i <= n; i++) {
				for (int j = 1; j <= n; j++) {
					ddd[i][j] = min(ddd[i][j], ddd[i][k]+ddd[k][j]);
				}
			}
		}
		vector< vector< vector<int> > > dp(n+1, vector< vector<int> >(n+1, vector<int>(c+1, INF)));
		for (int i = 1; i <= n; i++) {
			dp[s][i][0] = ddd[s][i];
		}
		for (int k = 1; k <= c; k++) {
			for (int p = 1; p <= n; p++) {
				dp[s][p][k] = dp[s][p][k-1];
				for (int i = 1; i <= n; i++) {
					if (dp[s][i][k-1] == INF) continue;
					for (int j = 1; j <= n; j++) {
						if (ddd[i][j] == INF) continue;
						for (int q = 0; q < ff[j].size(); q++) {
							if (ddd[ff[j][q].to][p] == INF) continue;
							if (dp[s][p][k] > dp[s][i][k-1]+ddd[i][j]+(ff[j][q].cost/2)+ddd[ff[j][q].to][p]) {
								dp[s][p][k] = dp[s][i][k-1]+ddd[i][j]+(ff[j][q].cost/2)+ddd[ff[j][q].to][p];
							}
						}/*
						for (int q = 1; q <= n; q++) {
							if (ddd[q][p] == INF) continue;
							if (ff[j][q] != INF) {
								if (dp[s][p][k] > dp[s][i][k-1]+ddd[i][j]+(ff[j][q]/2)+ddd[q][p]) {
									dp[s][p][k] = dp[s][i][k-1]+ddd[i][j]+(ff[j][q]/2)+ddd[q][p];
								}
							}
						}*/
					}
				}
			}
		}
		cout << dp[s][d][c] << endl;
	}
	return 0;
}