#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <iostream>
#include <math.h>
#include <assert.h>
#include <vector>
#include <queue>

using namespace std;
typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;
static const double EPS = 1e-9;
static const double PI = acos(-1.0);

#define REP(i, n) for (int i = 0; i < (int)(n); i++)
#define FOR(i, s, n) for (int i = (s); i < (int)(n); i++)
#define FOREQ(i, s, n) for (int i = (s); i <= (int)(n); i++)
#define FORIT(it, c) for (__typeof((c).begin())it = (c).begin(); it != (c).end(); it++)
#define MEMSET(v, h) memset((v), h, sizeof(v))

typedef int Weight;
struct Edge {
  int cnt;
  int src;
  int dest;
  Weight weight;
  Edge(int cnt, int src, int dest, Weight weight) : cnt(cnt), src(src), dest(dest), weight(weight) {;}
  bool operator<(const Edge &rhs) const {
    if (weight != rhs.weight) { return weight > rhs.weight; }
    return false;
  }
};
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;
typedef vector<Weight> Array;
typedef vector<Array> Matrix;

void PrintMatrix(const Matrix &matrix) {
  for (int y = 0; y < (int)matrix.size(); y++) {
    for (int x = 0; x < (int)matrix[y].size(); x++) {
      printf("%d ", matrix[y][x]);
    }
    puts("");
  }
}

int c, n, m, s, d;
bool visit[20][110];
int dist[20][110];

int main() {
  while (scanf("%d %d %d %d %d", &c, &n, &m, &s, &d), c|n|m|s|d) {
    MEMSET(visit, false);
    MEMSET(dist, 0x0f);
    s--; d--;
    Graph g(n);
    REP(i, m) {
      int f, t, cost;
      scanf("%d %d %d", &f, &t, &cost);
      f--; t--;
      g[f].push_back(Edge(0, f, t, cost));
      g[t].push_back(Edge(0, t, f, cost));
    }
    priority_queue<Edge> que;
    que.push(Edge(c, 0xdeadbeaf, s, 0));
    while (!que.empty()) {
      Edge e = que.top();
      que.pop();
      if (visit[e.cnt][e.dest]) { continue; }
      visit[e.cnt][e.dest] = true;
      if (e.dest == d) {
        printf("%d\n", e.weight);
        break;
      }
      FORIT(it, g[e.dest]) {
        if (e.cnt != 0) {
          int ncost = e.weight + it->weight / 2;
          if (ncost < dist[e.cnt - 1][it->dest]) {
            dist[e.cnt - 1][it->dest] = ncost;
            que.push(Edge(e.cnt - 1, 0xdeadbeaf, it->dest, ncost));
          }
        }
        int ncost = e.weight + it->weight;
        if (ncost < dist[e.cnt - 1][it->dest]) {
          dist[e.cnt][it->dest] = ncost;
          que.push(Edge(e.cnt, 0xdeadbeaf, it->dest, ncost));
        }
      }
    }
  }
}