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]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)
					}
				}
			}
		}
		runtime.GC()
	}
}

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;
};




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){
		vector<root> vr;
		ans=0;
		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]=1e8;
		}
		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<functional>
#include<queue>

#define INFTY 1<<30
#define N 101
#define C 11
#define CONNECTED 1
#define IN_QUEUE 1

using namespace std;

int cost[N][C];
bool vis[N][C];
int W[N][N];
int G[N][N];

class Node{
public:
	Node():id(0),cost(INFTY),c(0){}
	int id;
	int cost;
	int c;
	bool operator>(const Node &t)const{return this->cost > t.cost;}
};

void Dijkstra( Node s ){
	priority_queue<Node,vector<Node>,greater<Node>> pq;

	pq.push( s );

	while( !pq.empty() ){
		Node p = pq.top();

		pq.pop();

		if( vis[p.id][p.c] )
			continue;
		vis[p.id][p.c] = true;
		cost[p.id][p.c] = min( cost[p.id][p.c], p.cost );

		for(int i = 0; i < N; ++i){
			if( G[p.id][i] == CONNECTED ){
				Node np;

				np.id = i;
				np.cost = cost[p.id][p.c] + W[p.id][i];
				np.c = p.c;
				pq.push( np );
				if( p.c > 0 ){
					np.cost = cost[p.id][p.c] + (W[p.id][i]/2);
					np.c = p.c - 1;
					pq.push( np );
				}
			}
		}
	}
}
void ResetGraph(){
	for(int i = 0; i < N; ++i){
		for(int j = 0; j < C; ++j){
			cost[i][j] = INFTY;
			vis[i][j] = false;
		}
		for(int j = 0; j < N; ++j){
			G[i][j] = 0;
			W[i][j] = 0;
		}
	}
}
int main(){
	while( true ){
		int c, n, m, s, d;
		int ans = INFTY;
		Node start;
		
		cin >> c >> n >> m >> s >> d;
		if( !(c||n||m||s||d) )
			break;

		ResetGraph();
		for(int i = 0; i < m; ++i){
			int a, b, f;

			cin >> a >> b >> f;
			G[a][b] = G[b][a] = CONNECTED;
			W[a][b] = W[b][a] = f;
		}
		start.id = s;
		start.cost = 0;
		start.c = c;

		Dijkstra( start );

		for(int i = 0; i < C; ++i){
			ans = min(ans, cost[d][i]);
		}
		cout << ans << '\n';
	}
	return 0;
}