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]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 <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef long double ld;
typedef tuple<int, int> duo;

#define TT template<typename T>
#define TTF template<typename T, typename F>
#define ET(T) typename T::value_type
TT inline T sq(T x){return x*x;}
TT inline T In(){T x;cin>>x;return x;}
TT inline void Out(T&x){cout<<x;}
TT inline void sort(T&v){sort(begin(v),end(v));}
TT inline void revs(T&v){reverse(begin(v),end(v));}
TT inline void uniq(T&v){sort(v);v.erase(unique(begin(v),end(v)),end(v));}
TT inline int ubnd(T&v,ET(T)&x){return upper_bound(begin(v),end(v),x)-begin(v);}
TT inline int lbnd(T&v,ET(T)&x){return lower_bound(begin(v),end(v),x)-begin(v);}
TTF inline void inpt(T&v,int n,F f){for(v.reserve(n);n--;v.emplace_back(f()));}
TTF inline void show(T&v,F f,string d=" ",string e="\n"){int i=0;for(auto&x:v)i++&&(cout<<d),f(x);cout<<e;}
#undef TT
#undef TTF
#undef ET

inline void fast_io(){ios::sync_with_stdio(0);cin.tie(0);}
inline int in(){int x;scanf("%d",&x);return x;}
inline ll pow_mod(ll a,ll k,ll m){ll r=1;for(;k>0;a=a*a%m,k>>=1)if(k&1)r=r*a%m;return r;}
inline ll mod_inv(ll a,ll p){return pow_mod(a,p-2,p);}

const int dx[] = {0, 0, 1, -1, 1, 1, -1, -1};
const int dy[] = {1, -1, 0, 0, 1, -1, 1, -1};
const int Mod = 1000000000;

struct Edge {
  int f, t, w, c;
  Edge(int f, int t, int w, int c=0) : f(f), t(t), w(w), c(c) {}
  bool operator<(const Edge& e) const {
    return w != e.w ? w > e.w : (f != e.f ? f < e.f : (t != e.t ? t < e.t : c < e.c));
  }
};
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;

int dijkstra(const Graph& g, int s, int t, int c){
  int vis[128][16] = {};
  priority_queue<Edge> pq;
  for (pq.push(Edge(-2, s, 0)); !pq.empty(); pq.pop()){
    Edge e = pq.top();
    if (e.c > c) continue;
    if (vis[e.t][e.c]++) continue;
    if (e.t == t) return e.w;
    for (const auto& ee : g[e.t]){
      pq.push(Edge(e.t, ee.t, e.w + ee.w, e.c));
      pq.push(Edge(e.t, ee.t, e.w + ee.w / 2, e.c + 1));
    }
  }
  return -1;
}

int main()
{
  int c, n, m, s, d;
  while (cin >> c >> n >> m >> s >> d, c || n || m || s || d){
  Graph g(n + 1);
  for (int i = 0; i < m; i++){
    int a, b, f;
    cin >> a >> b >> f;
    g[a].push_back(Edge(a, b, f));
    g[b].push_back(Edge(b, a, f));
  }
  cout << dijkstra(g, s, d, c) << endl;
  }
  return (0);
}

// priority_queue queue deque front stringstream max_element min_element insert count make_tuple

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

using namespace std;

#define REP(i, n) for(int i=0; i<n; i++)

struct edge{
    int to, cost;
};

typedef pair<int, pair<int, int> > pii; // distance, edge, ticket

int INF = 10e8;
int c, n, m, s, d;

int dis[100][11];

int main(){
    while(1){
        cin >> c >> n >> m >> s >> d;

        if(n==0) break;

        vector<edge> g[100];
        REP(i, m){
            int a, b, f;
            cin >> a >> b >> f;
            edge ae;
            ae.to = b;
            ae.cost = f;
            g[a].push_back(ae);
            edge be;
            be.to = a;
            be.cost = f;
            g[b].push_back(be);
        }

        priority_queue<pii, vector<pii>, greater<pii> > que;
        REP(i, n+1){
            REP(j, c+1){
                dis[i][j] = INF;
            }
        }
        dis[s][c] = 0;
        pii init = make_pair(0, make_pair(s, c));
        que.push(init);

        while(!que.empty()){
            pii p = que.top();
            que.pop();

            int v = p.second.first;
            int t = p.second.second;
            if(dis[v][t]<p.first) continue;
            REP(i, g[v].size()){
                edge e = g[v][i];
                if(dis[e.to][t] > dis[v][t] + e.cost){
                    dis[e.to][t] = dis[v][t] + e.cost;
                    que.push(pii(make_pair(dis[e.to][t], make_pair(e.to, t))));
                }
                if(t>0){
                    if(dis[e.to][t-1] > dis[v][t] + e.cost / 2){
                        dis[e.to][t-1] = dis[v][t] + e.cost / 2;
                        que.push(pii(make_pair(dis[e.to][t-1], make_pair(e.to, t-1))));
                    }
                }
            }
        }
        /*
        REP(i, n+1){
            REP(j, c+1){
                cout << dis[i][j] << " ";
            }
            cout << endl;
        }
        */
        cout << dis[d][0] << endl;
    }
}