// 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;
  }
}