#include<bits/stdc++.h>
using namespace std;
typedef pair<int, int> pii;
typedef pair<int, pii> piii;//cost, v, ticket
struct edge{
  int to, cost;
};

int main(int argc, char *argv[]){
  int c, n, m, s, d;
  while(std::cin >> c >> n >> m >> s >> d, n){
    s--;d--;
    vector<vector<edge> > g(n);
    for (int i = 0; i < m; i++) {
      edge e;
      int from;
      std::cin >> from >> e.to >> e.cost;
      e.to--;from--;
      g[from].push_back(e);
      g[e.to].push_back((edge){from, e.cost});
    }
    vector<vector<int> > dp(c + 1, vector<int>(n, 1e9));
    dp[0][s] = 0;
    priority_queue<piii, vector<piii>, greater<piii> > que;
    que.push(piii(0, pii(s, 0)));
    while(!que.empty()){
      int cost   = que.top().first;
      int v      = que.top().second.first;
      int ticket = que.top().second.second;
      que.pop();
      for (int i = 0; i < g[v].size(); i++) {
        edge e = g[v][i];
        if(dp[ticket][e.to] > dp[ticket][v] + e.cost){
          dp[ticket][e.to] = dp[ticket][v] + e.cost;
          que.push(piii(dp[ticket][e.to], pii(e.to, ticket)));
        }
        if(ticket + 1 <= c &&
           dp[ticket + 1][e.to] > dp[ticket][v] + e.cost/2){
          dp[ticket + 1][e.to] = dp[ticket][v] + e.cost/2;
          que.push(piii(dp[ticket + 1][e.to],
                        pii(e.to, ticket + 1)));
        }
      }
    }
    std::cout << dp[c][d] << std::endl;
  }
  return 0;
}