#include<bits/stdc++.h>
using namespace std;

typedef long long int ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
typedef vector<pair<int, int> > vii;
#define rrep(i, m, n) for(int (i)=(m); (i)<(n);  (i)++)
#define erep(i, m, n) for(int (i)=(m); (i)<=(n); (i)++)
#define  rep(i, n)    for(int (i)=0; (i)<(n);  (i)++)
#define rrev(i, m, n) for(int (i)=(n)-1; (i)>=(m); (i)--)
#define erev(i, m, n) for(int (i)=(n); (i)>=(m); (i)--)
#define  rev(i, n)    for(int (i)=(n)-1; (i)>=0; (i)--)
#define vrep(i, c)    for(__typeof((c).begin())i=(c).begin(); i!=(c).end(); i++)
#define  ALL(v)       (v).begin(), (v).end()
#define pb            push_back
template<class T, class S> inline pair<T, S> mp(const T x, const S y){ return make_pair(x, y); }
template<class T, class S> inline bool minup(T& m, const S x){ return m>(T)x ? (m=(T)x, true) : false; }
template<class T, class S> inline bool maxup(T& m, const S x){ return m<(T)x ? (m=(T)x, true) : false; }

static const int    INF = 1000000000;
static const ll     MOD = 1000000007LL;
static const double EPS = 1E-10;

const int MAX_N = 111;
const int MAX_C = 22;
int c, n, m, s, d;
int t, u, f;
struct Edge{int from, to, cost;};
vector<Edge> g[MAX_N];
int l[MAX_N][MAX_C];

int main()
{
  while(cin >> c >> n >> m >> s >> d, c){
    rep(i, n) g[i].clear();
    rep(i, MAX_N) rep(j, MAX_C) l[i][j] = INF;

    rep(i, m){
      cin >> t >> u >> f;
      g[t - 1].pb((Edge){t - 1, u - 1, f});
      g[u - 1].pb((Edge){u - 1, t - 1, f});
    }

    priority_queue<vi, vector<vi>, greater<vi> > que;
    vi tmp(3);
    tmp[0] = 0;       // ?????¢
    tmp[1] = c;       // ?????°
    tmp[2] = s -  1;  // ??´???
    l[s - 1][c] = 0;
    que.push(tmp);
    while(!que.empty()){
      vi p = que.top();  que.pop();
      int ti = p[1];
      int v = p[2];
      if(l[v][ti] < p[0]) continue;

      vrep(w, g[v]){
        Edge& e = *w;
        if(l[e.to][ti] > l[v][ti] + e.cost){
          l[e.to][ti] = l[v][ti] + e.cost;
          tmp[0] = l[e.to][ti];
          tmp[1] = c;
          tmp[2] = e.to;
          que.push(tmp);
        }
      }

      if(c > 0) vrep(w, g[v]){
          Edge& e = *w;
          if(l[e.to][ti - 1] > l[v][ti] + e.cost / 2){
            l[e.to][ti - 1] = l[v][ti] + e.cost / 2;
            tmp[0] = l[e.to][ti - 1];
            tmp[1] = c - 1;
            tmp[2] = e.to;
            que.push(tmp);
          }
        }
    }

    cout << l[d - 1][0] << endl;
  }

  return 0;
}