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]struct{})
		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}] = struct{}{}
			for _, v := range pointMap[now.NowPosition] {
				next := &Node{v.NextPoint, now.DiscountTicketTCount, now.Amount + v.Fee}
				if _, ok := memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}]; !ok {
					heap.Push(&pq, next)
				}
				if now.DiscountTicketTCount > 0 {
					next = &Node{v.NextPoint, now.DiscountTicketTCount - 1, now.Amount + v.Fee/2}
					if _, ok := memo[Memo{NowPoint: v.NextPoint, DiscountTicketTCount: now.DiscountTicketTCount}]; !ok {
						heap.Push(&pq, next)
					}
				}
			}
		}
	}
}

C++: #include<iostream>
using namespace std;
#include<vector>
#include<queue>
//#include<math.h>
struct crq{
	int cost;
	int ticket;
	int now;

	bool operator > (const crq& p) const{
	return cost > p.cost;
	}
};//cost root que
struct root{
	int s;
	int g;
	int cost;
};



vector<root> vr;

int c;
int n;
int m;
int s;
int d;
int ans;
bool townSearched[100];
int townMin[100][11];

int main(){
	while(cin>>c>>n>>m>>s>>d, c|n|m|s|d){
		vr.clear();
		ans=INT_MAX;
		priority_queue<crq,vector<crq>,greater<crq>> q;
		while(!q.empty())q.pop();
		for(int  i=0;i<100;i++){
			townSearched[i]=false;
			for(int  j=0;j<11;j++)townMin[i][j]=INT_MAX;
		}
		for(int i=0;i<m;i++){
			root r;
			cin>>r.s;
			r.s--;
			cin>>r.g;
			r.g--;
			cin>>r.cost;
			vr.push_back(r);
		}
		townMin[s-1][c]=0;
		crq start;
		start.cost=0;
		start.ticket=c;
		start.now=s-1;

		q.push(start);
		while(1){
			crq crq2=q.top();q.pop();
			if(crq2.now==d-1){
				ans=crq2.cost;
				break;
			}
			

			for(int i=0;i<m;i++){
				if(vr.at(i).s==crq2.now){
					if(!townSearched[vr.at(i).g]&&townMin[vr.at(i).g][crq2.ticket]>crq2.cost+vr.at(i).cost){
						crq add;
						add.cost=crq2.cost+vr.at(i).cost;
						add.ticket=crq2.ticket;
						add.now=vr.at(i).g;
						townMin[vr.at(i).g][crq2.ticket]=crq2.cost+vr.at(i).cost;
						q.push(add);
					}

					if(!townSearched[vr.at(i).g]&&crq2.ticket>0&&townMin[vr.at(i).g][crq2.ticket-1]>crq2.cost+vr.at(i).cost/2){
						crq add;
						add.cost=crq2.cost+vr.at(i).cost/2;
						add.ticket=crq2.ticket-1;
						add.now=vr.at(i).g;
						townMin[vr.at(i).g][crq2.ticket]=crq2.cost+vr.at(i).cost/2;
						q.push(add);
					}

				}
				if(vr.at(i).g==crq2.now){
					if(!townSearched[vr.at(i).s]&&townMin[vr.at(i).s][crq2.ticket]>crq2.cost+vr.at(i).cost){
						crq add;
						add.cost=crq2.cost+vr.at(i).cost;
						add.ticket=crq2.ticket;
						add.now=vr.at(i).s;
						townMin[vr.at(i).s][crq2.ticket]=crq2.cost+vr.at(i).cost;
						q.push(add);
					}

					if(!townSearched[vr.at(i).s]&&crq2.ticket>0&&townMin[vr.at(i).s][crq2.ticket-1]>crq2.cost+vr.at(i).cost/2){
						crq add;
						add.cost=crq2.cost+vr.at(i).cost/2;
						add.ticket=crq2.ticket-1;
						add.now=vr.at(i).s;
						townMin[vr.at(i).s][crq2.ticket]=crq2.cost+vr.at(i).cost/2;
						q.push(add);
					}

				}
			}
			townSearched[crq2.now]=true;
		}
		cout<<ans<<endl;
	}
	return 0;
}

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;
	}