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++: // clang-format off
#include <bits/stdc++.h>
#define int long long
#define main signed main()
#define loop(i, a, n) for (int i = (a); i < (n); i++)
#define rep(i, n) loop(i, 0, n)
#define forever for (;;)
#define all(v) (v).begin(), (v).end()
#define rall(v) (v).rbegin(), (v).rend()
#define prec(n) fixed << setprecision(n)
typedef std::pair<int, int> pii;
typedef std::vector<int> vi;
typedef std::vector<double> vd;
typedef std::vector<std::string> vs;
typedef std::vector<pii> vpii;
typedef std::vector<vi> vvi;
typedef std::vector<vpii> vvpii;
const int INF = sizeof(int) == sizeof(long long) ? 1000000000000000000LL : 1000000000;
const int MOD = 1000000007;
const double PI = acos(-1);
template<typename A, typename B> bool cmin(A &a, const B &b) { return a > b ? (a = b, true) : false; }
template<typename A, typename B> bool cmax(A &a, const B &b) { return a < b ? (a = b, true) : false; }
template<typename T> std::istream &operator>>(std::istream &is, std::vector<T> &v) { rep(i,v.size()) is >> v[i]; return is; }
template<typename A, typename B> std::istream &operator>>(std::istream &is, std::pair<A, B> &p) { is >> p.first; is >> p.second; return is; }
using namespace std;
// clang-format on

typedef int Weight;
struct Edge {
  int src, dst;
  Weight weight;
  Edge(const int &s = 0, const int &d = 0, const Weight &w = 0) : src(s), dst(d), weight(w) {}
};

typedef std::vector<Edge> Edges;
typedef std::vector<Weight> Array;
typedef std::vector<Array> Matrix;

class Graph {
  std::vector<Edges> g;

public:
  Graph(const int &size = 0) : g(size) {}
  int size() const { return g.size(); }
  const Edges &operator[](const int &i) const { return g[i]; }
  void addArc(const int &src, const int &dst, const Weight &w = 1) { g[src].emplace_back(src, dst, w); }
  void addEdge(const int &node1, const int &node2, const Weight &w = 1) {
    addArc(node1, node2, w);
    addArc(node2, node1, w);
  }
};

template<int inf = std::numeric_limits<Weight>::max() / 8> std::pair<std::vector<Weight>, std::vector<int>> dijkstra(const Graph &g, const int &src) {
  using state = std::pair<Weight, int>;
  std::priority_queue<state, std::vector<state>, std::greater<state>> q;
  std::vector<Weight> dist(g.size(), inf);
  std::vector<int> via(g.size());
  dist[src] = 0;
  q.emplace(0, src);
  while (q.size()) {
    Weight d;
    int v;
    std::tie(d, v) = q.top();
    q.pop();
    if (dist[v] < d) continue;
    for (auto &e : g[v]) {
      if (cmin(dist[e.dst], dist[v] + e.weight)) {
        via[e.dst] = v;
        q.emplace(dist[e.dst], e.dst);
      }
    }
  }
  return {dist, via};
}
main {
  int c, n, m, s, d;
  while (cin >> c >> n >> m >> s >> d, c) {
    --s, --d;
    Graph g(n * (c + 1));
    while (m--) {
      int a, b, f;
      cin >> a >> b >> f;
      --a, --b;
      rep(i, c + 1) g.addEdge(a + n * i, b + n * i, f);
      rep(i, c) {
        g.addArc(n * i + a, n * (i + 1) + b, f / 2);
        g.addArc(n * i + b, n * (i + 1) + a, f / 2);
      }
    }
    vector<Weight> dist = dijkstra(g, s).first;
    int mini = INF;
    rep(i, c + 1) cmin(mini, dist[n * i + d]);
    cout << mini << endl;
  }
}

C++: #include <bits/stdc++.h>

using namespace std;

#define llong long long 
typedef pair<int, int> P;

typedef struct data{
	int now;
	int time;
	int dep;

	bool operator > (const data& right) const{
		return dep == right.dep ? time > right.time : dep > right.dep;
	}

}data;

int c, n, m, s, d;
vector<P> edges[101];
int cost[101][11];
priority_queue<data, vector<data>, greater<data> > q;

void solve(){
	data D;
	D.now = s;
	D.time = 0;
	D.dep = 0;
	q.push(D);

	while(!q.empty()){
		data nd = q.top(); q.pop();
		int nowp = nd.now;
		int nowtime = nd.time;
		int nowdep = nd.dep;

		if(cost[nowp][nowdep] < nowtime) continue;

		for(int i = 0; i < edges[nowp].size(); i++){
			P edge = edges[nowp][i];
			if(cost[edge.first][nowdep] > cost[nowp][nowdep] + edge.second){
				data in;
				in.now = edge.first;
				in.time = cost[nowp][nowdep] + edge.second;
				in.dep = nd.dep;
				cost[in.now][in.dep] = in.time;
				q.push(in);
			}

			if(nowdep < c){
				if(cost[edge.first][nowdep + 1] > cost[nowp][nowdep] + edge.second / 2){
					data in;
					in.now = edge.first;
					in.time = nowtime + (edge.second / 2);
					in.dep = nowdep + 1;
					cost[in.now][in.dep] = in.time;
					q.push(in);
				}			
			}

		}
	}

	return;
}

int main(){
	while(cin >> c >> n >> m >> s >> d, n){
		fill_n(*cost, 101 * 11, 99999999);
		for(int i = 0; i <= c; i++){
			cost[s][i] = 0;
		}
		for(int i = 0; i < m; i++){
			int n, to, cos;
			cin >> n >> to >> cos;
			edges[n].push_back(P(to, cos));
			edges[to].push_back(P(n, cos));
		}

		solve();

		cout << cost[d][c] << endl;
		// for(int i = 1; i <= n; i++){
		// 	cout << cost[i][2] << endl;
		// }

		for(int i = 0; i < 101; i++){
			edges[i].clear();
		}
	}

	return 0;
}