#include <iostream>
#include <vector>
#include <queue>
using namespace std;
 
#define MAX 10000000
#define n_MAX 101
#define c_MAX 11

typedef pair<int, pair<int, int> > edge;

inline int get_cost(edge e){
  return e.first;
}

inline int get_tickets(edge e){
  return -(e.second.first);
}

inline int get_station(edge e){
  return e.second.second;
}

inline edge make_edge(int cost, int tickets, int station){
  return make_pair(cost, make_pair(-tickets, station));
}

int main() {
 
  while( true ) {
    
    long long int c, n, m, s, d;
    cin >> c >> n >> m >> s >> d;
    if ( n == 0 ) break;
    
    long long int l[n_MAX][n_MAX] = {0};
    
    for ( long long int i = 0; i < m; i++ ) {
      long long int a, b, f;
      cin >> a >> b >> f;
      l[a][b] = l[b][a] = f;
    }
 
    long long int t[c_MAX][n_MAX];
    for ( long long int j = 0; j <= c; j++ ) {
      for ( long long int i = 1; i <= n; i++ ) {
	t[j][i] = MAX;
      }
    }
    
    priority_queue<edge, vector<edge>, less<edge> > queue;
    queue.push(make_edge(0, c, s));
    t[c][s] = 0;

    int ans = MAX;
    while(!queue.empty()){
      edge e = queue.top(); queue.pop();

      const int cost = get_cost(e);
      const int tickets = get_tickets(e);
      const int station = get_station(e);
      if(t[tickets][station] > cost){
	continue;
      }else if(station == d){
	ans = min(ans, cost);
      }
      

      for(long long int next = 1; next <= n; next++){
	if(l[station][next] == 0){
	  continue;
	}
	
	const int next_non_use_cost = cost + l[station][next];
	const int next_use_cost = cost + l[station][next] / 2;
 
	if(tickets > 0 && t[tickets - 1][next] > next_use_cost){
	  t[tickets - 1][next] = next_use_cost;
	  queue.push(make_edge(next_use_cost, tickets - 1, next));
	}
	
	if(t[tickets][next] > next_non_use_cost){
	  t[tickets][next] = next_non_use_cost;
	  queue.push(make_edge(next_non_use_cost, tickets, next));
	}
      }
    }
 
    cout << ans << endl;
  }
 
  return 0;
 
}