
#include<bits/stdc++.h>
using namespace std;
#define inf 1000000000
#define INF 1000000000000000
#define ll long long
#define ull unsigned long long
#define M (int)(1e9+7)
#define P pair<int,int>
#define PLL pair<ll,ll>
#define FOR(i,m,n) for(int i=(int)m;i<(int)n;i++)
#define RFOR(i,m,n) for(int i=(int)m;i>=(int)n;i--)
#define rep(i,n) FOR(i,0,n)
#define rrep(i,n) RFOR(i,n,0)
#define all(a) a.begin(),a.end()
#define IN(a,n) rep(i,n){ cin>>a[i]; }
const int vx[4] = {0,1,0,-1};
const int vy[4] = {1,0,-1,0};
#define PI 3.14159265
#define F first
#define S second
#define PB push_back
#define EB emplace_back
#define int ll
void init(){
  cin.tie(0);
  ios::sync_with_stdio(false);
}



template< typename T >
struct edge {
  int src, to;
  T cost;

  edge(int to, T cost) : src(-1), to(to), cost(cost) {}

  edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};

template< typename T >
using Edges = vector< edge< T > >;
template< typename T >
using WG = vector< Edges< T > >;
using UG = vector< vector< int > >;
template< typename T >
using Matrix = vector< vector< T > >;



template< typename T >
vector<T> dijkstra(WG<T> &g,int s){
  const auto lim = numeric_limits<T>::max();
  vector<T> dist(g.size(),lim);
  using Pi = pair<T,int>;
  priority_queue<Pi,vector<Pi>,greater<Pi>> q;
  dist[s] = 0;
  q.emplace(dist[s],s);
  while(!q.empty()){
    T cost;
    int idx;
    tie(cost,idx) = q.top();
    q.pop();
    if(dist[idx] < cost) continue;
    for( auto &e : g[idx]){
      auto next_cost = cost + e.cost;
      if(dist[e.to] <= next_cost) continue;
      dist[e.to] = next_cost;
      q.emplace(dist[e.to],e.to);
    }
  }
  return dist;
}


int c,n,m,s,d;

main(){
  while(true){
    cin>>c>>n>>m>>s>>d;
    if(n==0) break;

    s--;d--;
    WG<int> es(n*(c+1));

    rep(k,m){
      int a,b,f;
      cin>>a>>b>>f;
      a--;b--;
      rep(i,c+1){
        es[a*(c+1)+i].PB(edge<int>(b*(c+1)+i,f));
        es[b*(c+1)+i].PB(edge<int>(a*(c+1)+i,f));
      }
      FOR(i,1,c+1){
        es[a*(c+1)+i].PB(edge<int>(b*(c+1)+i-1,f/2));
        es[b*(c+1)+i].PB(edge<int>(a*(c+1)+i-1,f/2));
      }
    }

    vector<int> res=dijkstra(es,s*(c+1)+c);

    int ans=INF;
    rep(i,c+1){
      //cout<<res[d*(c+1)+i]<<endl;
      ans=min(ans,res[d*(c+1)+i]);
    }

    cout<<ans<<endl;

  }
}




