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 <queue>
#include <functional>
#include <algorithm>
#include <cstring>
#include <vector>
#include <map>

const int MAX_V = 101;
const int INF = 0x3f3f3f3f;

//??? T???cap??????rev????????°???????????§?????£???????????????
struct Edge{
	int to;
	int cost;
	Edge(int to_, int cost_) :to(to_), cost(cost_){}
};

std::vector<Edge > G[MAX_V]; //??£??\?????????

int d[11][MAX_V]; //[?????¨???????????±??????????????°][?????????]
int pre[MAX_V];

void AddEdge(int from, int to, int cost){
	G[from].push_back(Edge(to, cost));
}

void ClearEdge(){
	for (int i = 0; i < MAX_V; ++i) G[i].clear();
	memset(d, 0, sizeof(d));
	memset(pre, -1, sizeof(pre));
}

void Dijkstra(int c, int s){
	typedef std::pair<int, int> P; //first:???????????¢, second:????????????

	std::priority_queue<P, std::vector<P>, std::greater<P> > q;
	std::fill(d[c], d[c] + MAX_V, INF);
	memset(pre, -1, sizeof(pre));
	d[c][s] = 0;
	q.push(P(0, s));

	while (!q.empty()){
		P p = q.top(); q.pop();
		int from = p.second;
		if (d[c][from] < p.first) continue;
		for (Edge e : G[from]){
			int dmin;
			if (c == 0)
				dmin = d[c][from] + e.cost;
			else
				dmin = std::min(d[c][from] + e.cost, d[c - 1][from] + e.cost / 2);

			if (d[c][e.to] > dmin){
				d[c][e.to] = dmin;
				q.push(P(d[c][e.to], e.to));
				pre[e.to] = from;
			}
		}
	}
}

std::vector<int> GetPath(int t){
	std::vector<int> path;
	for (; t != -1; t = pre[t]) path.push_back(t);
	std::reverse(path.begin(), path.end());

	return path;
}

using namespace std;

int main(void){
	int c, n, m, s, g;
	while (1){
		cin >> c >> n >> m >> s >> g;
		if (c == n && n == m && m == s && s == g && g == 0) return 0;
		int a, b, f;
		for (int i = 0; i < m; ++i){
			cin >> a >> b >> f;
			AddEdge(a, b, f);
			AddEdge(b, a, f);
		}
		for (int i = 0; i <= c; ++i){
			Dijkstra(i, s);
		}
		cout << d[c][g] << endl;
		ClearEdge();
	}
}

C++: #include <iostream>
#include <vector>
#include <queue>
#include <utility>
using namespace std;

int calcCost(int c, int n, vector<int> path, vector<int> rt){
	priority_queue<int> costs;
	for(int i=1; i<rt.size(); i++){
		costs.push(path[rt[i]+n*rt[i-1]]);
	}
	int total = 0;
	while(costs.size() && c--){
		total += costs.top() / 2;
		costs.pop();
	}
	while(costs.size()){
		total += costs.top();
		costs.pop();
	}
	return total;
}

int main(){
	for(;;){
		int c,n,m,s,d;
		cin>>c>>n>>m>>s>>d;
		if(c+n+m+s+d==0) break;
		vector<pair<int, vector<int>>> route(n,make_pair(-1,vector<int>(0)));
		vector<int> path(n*n,-1);
		for(int i=0; i<m; i++){
			int a,b,f;
			cin>>a>>b>>f;
			path[--a+n*--b] = path[b+n*a] = f;
		}
		priority_queue<pair<int, vector<int>>, vector<pair<int, vector<int>>>, greater<pair<int, vector<int>>>> pq;
		pq.push(make_pair(0,vector<int>(1,s-1)));
		while(pq.size()){
			int cur = *(pq.top().second.rbegin());
			if(route[cur].first == -1){
				route[cur] = pq.top();
				for(int i=0; i<m; i++){
					if(route[i].first == -1 && path[i+n*cur] != -1){
						auto copy = pq.top();
						copy.second.push_back(i);
						copy.first = calcCost(c,n,path,copy.second);
						pq.push(copy);
					}
				}
			}
			pq.pop();
		}
		cout<<route[d-1].first<<endl;
	}
}

C++: #include<iostream>
#include<string>
#include<iomanip>
#include<cmath>
#include<vector>
#include<algorithm>
#include<queue>

using namespace std;

// http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=0212

#define int long long
#define rep(i,n) for(int i = 0; i < (n); i++)
#define INF ((long long)1e18)
#define MOD ((int)1e9+7)
#define endl "\n"

#define yn(f) ((f)?"Yes":"No")
#define YN(f) ((f)?"YES":"NO")

#define MAX_VAL 110
#define MAX_C 12

typedef long long ll;
typedef pair<pair<ll,ll>,int> P;

struct edge{ll to, cost;};


int dijkstra(vector<edge> G[MAX_VAL], int s, int g, int V, int c){
	priority_queue<P,vector<P>,greater<P>> q;
	ll d[MAX_C][MAX_VAL];
	
	for(int i = 0; i < MAX_C; i++) for(int j = 0; j < MAX_VAL; j++) d[i][j] = INF;
	
	d[0][s] = 0;
	q.push(P(make_pair(0,s),0));
	
	while(!q.empty()){
		P p = q.top();q.pop();
		ll v = p.first.second;
		
		if(v == g) return d[p.second][v];
		
		if(d[p.second][v] < p.first.first) continue;
		
		for(edge e : G[v]){
			if(d[p.second][e.to] > d[p.second][v] + e.cost){
				d[p.second][e.to] = d[p.second][v] + e.cost;
				q.push(P(make_pair(d[p.second][e.to],e.to),p.second));
			}
			if(c > p.second && d[p.second+1][e.to] > d[p.second][v] + e.cost/2){
				d[p.second+1][e.to] = d[p.second][v] + e.cost/2;
				q.push(P(make_pair(d[p.second+1][e.to],e.to),p.second+1));
			}
		}
	}
	
	// int res = INF;
	
	// for(int i = 0; i <= c; i++){
		// res = min(res,d[i][g]);
	// }
	// return res;
}

signed main(){
	// cin.tie(0);
	// ios::sync_with_stdio(false);
	cout<<fixed<<setprecision(10);
	
	int c, n, m, s, d;
	int a, b, f;
	edge temp;
	
	
	while(true){
		vector<edge> G[MAX_VAL];
		
		cin>>c>>n>>m>>s>>d;
		
		if(!c&&!n&&!m&&!s&&!d) break;
		
		for(int i = 0; i < m; i++){
			cin>>a>>b>>f;
			temp.cost = f, temp.to = b;
			G[a].push_back(temp);
			temp.to = a;
			G[b].push_back(temp);
		}
		
		cout<<dijkstra(G,s,d,n,c)<<endl;
	}
	
	return 0;
}