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)
template<typename A> using V = std::vector<A>;
template<typename A> using F = std::function<A>;
template<typename A, typename B> using P = std::pair<A, B>;
using pii = P<int, int>;
using vi = V<int>;
using vd = V<double>;
using vs = V<std::string>;
using vpii = V<pii>;
using vvi = V<vi>;
using vvpii = V<vpii>;
constexpr int INF = sizeof(int) == sizeof(long long) ? 1000000000000000000LL : 1000000000;
constexpr int MOD = 1000000007;
constexpr double PI = 3.14159265358979;
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; }
constexpr bool odd(const int n) { return n & 1; }
constexpr bool even(const int n) { return ~n & 1; }
template<typename T> std::istream &operator>>(std::istream &is, std::vector<T> &v) { for (T &x : v) is >> x; 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

using Weight = int;
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) {}
};

using Edges = vector<Edge>;
using Array = vector<Weight>;
using Matrix = vector<Array>;

class Graph {
  vector<Edges> g;
  using iterator = vector<Edges>::iterator;
  using const_iterator = vector<Edges>::const_iterator;

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);
  }
  iterator begin() { return g.begin(); }
  const_iterator begin() const { return g.begin(); }
  iterator end() { return g.end(); }
  const_iterator end() const { return g.end(); }
};

template<int inf = numeric_limits<Weight>::max() / 8> vector<Weight> dijkstra(const Graph &g, int num, const int src) {
  using state = tuple<Weight, int, int>; // weight, vertex, num
  priority_queue<state, vector<state>, greater<state>> q;
  V<V<Weight>> dist(g.size(), V<Weight>(num + 1, inf));
  dist[src][num] = 0;
  q.emplace(0, src, num);
  while (q.size()) {
    Weight d;
    int v;
    int k;
    tie(d, v, k) = q.top();
    q.pop();
    if (dist[v][k] < d) continue;
    for (auto &e : g[v]) {
      if (cmin(dist[e.dst][k], dist[v][k] + e.weight)) q.emplace(dist[e.dst][k], e.dst, k);
      if (k && cmin(dist[e.dst][k - 1], dist[v][k] + e.weight / 2)) q.emplace(dist[e.dst][k - 1], e.dst, k - 1);
    }
  }
  V<Weight> ans(g.size(), inf);
  rep(i, g.size()) rep(j, num + 1) cmin(ans[i], dist[i][j]);
  return ans;
}

main {
  int c, n, m, s, d;
  while (cin >> c >> n >> m >> s >> d, c + n + m + s + d) {
    --s, --d;
    Graph g(n);
    rep(_, m) {
      int a, b, f;
      cin >> a >> b >> f;
      g.addEdge(--a, --b, f);
    }
    vector<Weight> dist = dijkstra(g, c, s);
    cout << dist[d] << endl;
  }
}

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

using namespace std;

#define loop(i,a,b) for(int i=(a); i<(int)(b); i++)
#define rep(i,b) loop(i,0,b)

struct edge {
    int to, cost;
};

struct state {
    int v, d, rest;
    bool operator<(const state& s)const{
        return d>s.d;
    }
};

int dijk(int s, int g, const vector<vector<edge>>& G, int c){

    vector<int> d(G.size(), 1000000000);
    d[s] = 0;

    priority_queue<state> q;
    q.push({ s, 0, c });

    vector<vector<bool>> vis(G.size(), vector<bool>(c + 1, false));

    while (q.size()){
        state sta = q.top();
        q.pop();

        int v = sta.v;

        int rest = sta.rest;

        if (vis[v][rest]) continue;
        vis[v][rest] = true;

        rep(i, G[v].size()){

            int to = G[v][i].to;
            int cost = G[v][i].cost;


            if (d[to] > sta.d + cost){

                d[to] = sta.d + cost;
                q.push({ to, sta.d + cost, rest });
            }

            if (d[to] > sta.d + cost / 2 && rest != 0){

                d[to] = sta.d + cost / 2;
                q.push({ to, sta.d + cost / 2, rest - 1 });
            }
        }
    }
    return d[g];
}

int main(){
    while (1){
        int c, V, E, s, d;
        cin >> c >> V >> E >> s >> d;
        if (c == 0) break;
        vector<vector<edge>> G(V);
        s--; d--;
        rep(i, E){
            int a, b, c;
            cin >> a >> b >> c;
            a--; b--;
            G[a].push_back({ b, c });
            G[b].push_back({ a, c });
        }
        cout << dijk(s, d, G, c) << endl;
    }
}