#include <bits/stdc++.h>
#define PB push_back
#define MP make_pair
#define REP(i,n) for (int i=0;i<(n);i++)
#define FOR(i,a,b) for(int i=(a);i<(b);i++)
#define ALL(a) (a).begin(),(a).end()
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> P;
double EPS=1e-10;
int INF=1e9;
static const int MEM_SIZE=1000000;
struct edge{int to,cost;};
struct dat{
      int s,cost,num;
      dat(int s,int cost,int num):s(s),cost(cost),num(num){}
      bool operator<(const dat& a)const{return cost<a.cost;}
};
vector<edge> G[100];
int dist[100][11];
int n,c;
void dijkstra(int s){
      REP(i,100)REP(j,11)dist[i][j]=INF;
      priority_queue<dat>Q;
      Q.push(dat(s,0,0));
      dist[s][0]=0;
      while(!Q.empty()){
            dat p=Q.top();Q.pop();
            REP(i,G[p.s].size()){
                  edge e=G[p.s][i];
                  if(p.num<c){
                        if(dist[p.s][p.num]+e.cost/2<dist[e.to][p.num+1]){
                              dist[e.to][p.num+1]=dist[p.s][p.num]+e.cost/2;
                              Q.push(dat(e.to,dist[e.to][p.num+1],p.num+1));
                        }
                  }
                  if(dist[p.s][p.num]+e.cost<dist[e.to][p.num]){
                        dist[e.to][p.num]=dist[p.s][p.num]+e.cost;
                        Q.push(dat(e.to,dist[e.to][p.num],p.num));
                  }
            }
      }
}
int main(){
      int m,s,d;
      while(cin>>c>>n>>m>>s>>d&&(c||n||m||s||d)){
            s--;d--;
            REP(i,100)G[i].clear();
            REP(i,m){
                  int a,b,f;
                  cin>>a>>b>>f;
                  a--;b--;
                  G[a].PB((edge){b,f});
                  G[b].PB((edge){a,f});
            }
            dijkstra(s);
            int ans=INF;
            REP(i,c+1)ans=min(ans,dist[d][i]);
            cout<<ans<<endl;
      }
}