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 <cstdio>
#include <algorithm>
#include <queue>

#define INF (1e+9)

#define MAX_N 100
#define MAX_C 10

using namespace std;

typedef struct edge{
	int to;
	int cost;
	int used;
	edge(){}
	edge(int _to,int _cost,int _used){
		to = _to;
		cost = _cost;
		used = _used;
	}
	bool operator<(const edge &a)const{
		if(cost == a.cost) return to > a.to;
		return cost > a.cost;	//for ASC
	}
}edge;


int cost[MAX_N + 1][MAX_N + 1];
int sum[MAX_N + 1][MAX_C + 1];
priority_queue<edge > pque;

int C;
int N,M;
int S,D;

void init(){
	for(int i = 0;i <= MAX_N;i++){
		for(int j = 0;j <= MAX_N;j++){
			cost[i][j] = INF;
		}
	}
	for(int i = 0;i <= MAX_N;i++){
		for(int j = 0;j <= MAX_C;j++){
			sum[i][j] = INF;
		}
	}
	return ;
}

int solve(){
	int res;

	pque.push(edge(S,0,0));

	while(!pque.empty()){
		edge e = pque.top();pque.pop();
		if(sum[e.to][e.used] != INF) continue;
		sum[e.to][e.used] = e.cost;
		for(int i = 1;i <= N;i++){
			if(cost[e.to][i] != INF){
				int _cost = e.cost + cost[e.to][i];
				pque.push(edge(i,_cost,e.used));
				if(e.used < C){
					_cost = e.cost + cost[e.to][i] / 2;
					pque.push(edge(i,_cost,e.used + 1));
				}
			}
		}
	}

	res = INF;
	for(int i = 0;i <= 10;i++){
		res = min(res,sum[D][i]);
	}

	return res;
}

int main(){

	while(true){
		init();
		scanf("%d%d%d%d%d",&C,&N,&M,&S,&D);
		if(C == 0) break;
		int _u,_v,_cost;
		for(int i = 0;i < M;i++){
			scanf("%d%d%d",&_u,&_v,&_cost);
			cost[_u][_v] = _cost;
			cost[_v][_u] = _cost;
		}
		
		int ans = solve();

		/*for(int i = 1;i <= N;i++){
			printf("###");
			for(int j = 0;j <= C;j++){
				printf(" %d",sum[i][j]);
			}
			puts("");
		}*/
		printf("%d\n",ans);

	}

	return 0;
}

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;
typedef pair < P, int > PP;
#define f first
#define s second

//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 << 29;
int c, n, m, s, d, ans;
int tocost[101][11];
vector<P> town[1000];
priority_queue<PP, vector<PP>, greater<PP> > pq;


void dijkstra(){
	while (!pq.empty()){
		PP a = pq.top();
		pq.pop();
		for (int i = 0; i < town[a.f.s].size(); i++){
			int tt = town[a.f.s][i].f, cc = town[a.f.s][i].s;
			if (tocost[tt][a.s] > cc + a.f.f){
				tocost[tt][a.s] = cc + a.f.f;
				pq.push({ { cc + a.f.f, tt }, a.s });
			}
			if (a.s&&tocost[tt][a.s-1] > cc/2 + a.f.f){
				tocost[tt][a.s-1] = cc/2 + a.f.f;
				pq.push({ { cc / 2 + a.f.f, tt }, a.s - 1 });
			}
		}
	}
}
	int main(){
		while (cin >> c >> n >> m >> s >> d&&c&&n&&m&&s){
			for (int i = 0; i < 101; i++)
				fill(tocost[i], tocost[i] + 11, INF);
			tocost[s][c] = 0;
			ans = INF;
			while (pq.size())
				pq.pop();
			for (int i = 0; i < n; i++)
				town[i].clear();
			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;
	}

C++: #include <iostream>
#include <cstdio>
#include <cmath>
#include <vector>
#include <map>
#include <queue>
#include <algorithm>
#include <utility>
#include <cstring>
#include <string>
#include <sstream>

#define rep(i, n) for(int i = 0; i < n; i ++)
#define ALL(T) T.begin(), T.end()

using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
typedef vector<vector<int> > table;

int n;
const int INF = (int)1e7;
const int N = 100;
const int C = 11;
table cost(N);
vector<vector<bool> > used(11);

int dijkstra(int, int, int);

int main(void){
    rep(i, N) cost[i].resize(N);
    rep(i, C) used[i].resize(N);

    for(int c, m, s, g; cin >> c >> n >> m >> s >> g, n; cout << dijkstra(s, g, c) << endl){
        rep(i, N) fill(ALL(cost[i]), INF);
        rep(i, C) fill(ALL(used[i]), false);

        while(m --){
            int a, b, f; cin >> a >> b >> f;
            
            cost[a - 1][b - 1] = cost[b - 1][a - 1] = f;
        }
    }
    
    return 0;
}

int dijkstra(int s, int g, int c){
    table d(c + 1);
    rep(i, c + 1) d[i].resize(n), fill(ALL(d[i]), INF);
    
    d[c][s - 1] = 0;

    while(1){
        int vn = -1, vc = -1;

        rep(i, c + 1) rep(j, n) if(!used[i][j] && (vc == -1 || d[i][j] < d[vc][vn])) vc = i, vn = j;

        if(vc == -1) break;
        used[vc][vn] = true;

        rep(u, n){
            d[vc][u] = min(d[vc][u], d[vc][vn] + cost[vn][u]);
            if(vc) d[vc - 1][u] = min(d[vc - 1][u], d[vc][vn] + cost[vn][u] / 2);
        }
    }

    return d[0][g - 1];
}