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

const double PI = acos(-1);
const double EPS = 1e-15;
using ll = long long;
using ull = unsigned long long;
const int inf = 2e9;
const ll INF = 2e18;
const ll MOD = 1e9+7;
const ll MOD1 = 998244353;
typedef pair<int,int> P;

#define REP(i,n) for (int i = 0; i < (n); i++)
#define sz(s) (s).size()
#define pb push_back
#define fi first
#define se second
#define mp make_pair

int main(){
  int c,n,m,s,d;
  while (cin >> c >> n >> m >> s >> d,c,n,m,s,d) {
    ll dp[110][11];
    REP(i,110) REP(j,11) dp[i][j] = INF;
    s--;
    d--;
    vector<pair<int,ll>> G[110];
    REP(i,m) {
      int a,b;
      ll f;
      cin >> a >> b >> f;
      a--;
      b--;
      G[a].pb({b,f});
      G[b].pb({a,f});
    }
    priority_queue<pair<ll,pair<int,int>>,vector<pair<ll,pair<int,int>>>,greater<pair<ll,pair<int,int>>>> pq;
    dp[s][0] = 0;
    pq.push({0,{s,0}});
    while (!pq.empty()) {
      pair<ll,pair<int,int>> tp = pq.top();
      //cout << tp.fi << " " << tp.se.fi << " " << tp.se.se << endl;
      pq.pop();
      int point = tp.se.fi;
      int ticket = tp.se.se;
      if (tp.fi > dp[point][ticket]) continue;
      //cout << "test" << endl;
      REP(i,sz(G[point])) {
        int next = G[point][i].fi;
        ll cost = G[point][i].se;
        if (dp[point][ticket] + cost < dp[next][ticket]) {
          dp[next][ticket] = dp[point][ticket] + cost;
          pq.push({dp[next][ticket],{next,ticket}});
        }
        if (dp[point][ticket] + cost/2 < dp[next][ticket+1]) {
          dp[next][ticket+1] = dp[point][ticket] + cost/2;
          pq.push({dp[next][ticket+1],{next,ticket+1}});
        }
      }
    }
    ll ans = INF;
    REP(i,c+1) {
      ans = min(ans,dp[d][i]);
    }
    cout << dp[d][c] << endl;
  }
  return 0;
}


