#include <bits/stdc++.h>
using namespace std;
#define repl(i,a,b) for(int i=(int)(a);i<(int)(b);i++)
#define rep(i,n) repl(i,0,n)
#define mp(a,b) make_pair((a),(b))
#define pb(a) push_back((a))
#define all(x) (x).begin(),(x).end()
#define uniq(x) sort(all(x)),(x).erase(unique(all(x)),end(x))
#define fi first
#define se second
#define dbg(...) _dbg(#__VA_ARGS__, __VA_ARGS__)
void _dbg(string){cout<<endl;}
template<class H,class... T> void _dbg(string s,H h,T... t){int l=s.find(',');cout<<s.substr(0,l)<<" = "<<h<<", ";_dbg(s.substr(l+1),t...);}
template<class T,class U> ostream& operator<<(ostream& o, const pair<T,U> &p){o<<"("<<p.fi<<","<<p.se<<")";return o;}
template<class T> ostream& operator<<(ostream& o, const vector<T> &v){o<<"[";for(T t:v){o<<t<<",";}o<<"]";return o;}

#define INF 1120000000

int main(){
  using P = pair<int,int>;
  int c,n,m,s,t;
  while(cin>>c>>n>>m>>s>>t, c|n|m){
    s--;t--;
    vector<vector<P>> vec(n);
    rep(i,m){
      int a,b,f;
      cin>>a>>b>>f;
      a--;b--;
      vec[a].pb(mp(f,b));
      vec[b].pb(mp(f,a));
    }

    vector<vector<int>> d(m,vector<int>(c+1,INF));
    priority_queue<P, vector<P>, greater<P>> pq;
    pq.push(mp(0,s*(c+1)));
    d[s][c] = 0;
    while(!pq.empty()){
      auto p = pq.top(); pq.pop();
      int v = p.se/(c+1);
      int k = p.se%(c+1);
      if(d[v][k] < p.fi) continue;

      auto go = [&](int nv, int nk, int dist){
        if(d[nv][nk] > dist){
          pq.push(mp(dist, nv*(c+1)+nk));
          d[nv][nk] = dist;
        }
      };

      for(auto to : vec[v]){
        go(to.se, k, p.fi + to.fi);
        if(k<c) go(to.se, k+1, p.fi + to.fi/2);
      }
    }

    cout << *min_element(all(d[t])) << endl;
  }

  return 0;
}