#include<bits/stdc++.h>
#define F first
#define S second
#define INF 1<<28
using namespace std;

int c, n, s, d;
typedef pair < int, int > P;
typedef pair < int, P > PP;
vector < P > vec[111];

int solve(){

  int dist[111][11]; for(int i=0;i<111;i++)for(int j=0;j<11;j++) dist[i][j] = INF;
  priority_queue < PP, vector<PP>, greater<PP> > que;

  dist[s][c] = 0;
  que.push( PP(0, P(s, c)) ); //Now_cost, Now_node, Now_ticket

  while(!que.empty()){
    PP p = que.top(); que.pop();
    int cost = p.F, now = p.S.F, tic = p.S.S;

    //if(dist[now][tic] < cost) continue;
    for(int i=0;i<vec[now].size();i++){
      P to = vec[now][i];
      if(dist[to.S][tic] > dist[now][tic] + to.F){
	dist[to.S][tic] = dist[now][tic] + to.F;
	que.push( PP(dist[to.S][tic], P(to.S, tic)) );
      }
      if(tic && dist[to.S][tic-1] > dist[now][tic] + to.F/2){
	dist[to.S][tic-1] = dist[now][tic] + to.F/2;
	que.push( PP(dist[to.S][tic-1], P(to.S, tic-1)) );
      }
    }
  }
  
  int ans = INF;
  for(int i=0;i<=c;i++){ ans = min(ans, dist[d][i]); } //cout << ans << endl; }
  return ans;
}

int main(){

  int m, a, b, p;

  
  while(cin >> c >> n >> m >> s >> d){
    if((c|n|m|s|d) == 0) break;
    for(int i=0;i<111;i++) vec[i].clear();
    for(;m--;){
      cin >> a >> b >> p;
      vec[a].push_back(P(p, b)); //[now] P(cost, next);
      vec[b].push_back(P(p, a));
    }
    
    cout << solve() << endl;
  }
  
}