#include <iostream>
#include <vector>
#include <algorithm>
#include <map>
#include <set>
#include <queue>
#include <numeric>

using namespace std;
using ll = long long;
using ull = unsigned long long;

#define REP(i,n) for(long long i = 0; i < (n); i++)
#define FOR(i, m, n) for(long long i = (m);i < (n); ++i)
#define ALL(obj) (obj).begin(),(obj).end()
#define SPEED cin.tie(0);ios::sync_with_stdio(false);

template<class T> using V = vector<T>;
template<class T, class U> using P = pair<T, U>;

const ll MOD = (ll)1e9 + 7;
const ll MOD2 = 998244353;
const ll HIGHINF = (ll)1e18;
const ll LOWINF = (ll)1e15;
const long double PI = 3.1415926535897932384626433;

template <class T> void corner(bool flg, T hoge) {if (flg) {cout << hoge << endl; exit(0);}}
template <class T, class U>ostream &operator<<(ostream &o, const map<T, U>&obj) {o << "{"; for (auto &x : obj) o << " {" << x.first << " : " << x.second << "}" << ","; o << " }"; return o;}
template <class T>ostream &operator<<(ostream &o, const set<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;}
template <class T>ostream &operator<<(ostream &o, const multiset<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;}
template <class T>ostream &operator<<(ostream &o, const vector<T>&obj) {o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "") << obj[i]; o << "}"; return o;}
template <class T, class U>ostream &operator<<(ostream &o, const pair<T, U>&obj) {o << "{" << obj.first << ", " << obj.second << "}"; return o;}
template <template <class tmp>  class T, class U> ostream &operator<<(ostream &o, const T<U> &obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr)o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;}
void print(void) {cout << endl;}
template <class Head> void print(Head&& head) {cout << head;print();}
template <class Head, class... Tail> void print(Head&& head, Tail&&... tail) {cout << head << " ";print(forward<Tail>(tail)...);}
template <class T> void chmax(T& a, const T b){a=max<T>(a,b);}
template <class T> void chmin(T& a, const T b){a=min<T>(a,b);}
void YN(bool flg) {cout << ((flg) ? "YES" : "NO") << endl;}
void Yn(bool flg) {cout << ((flg) ? "Yes" : "No") << endl;}
void yn(bool flg) {cout << ((flg) ? "yes" : "no") << endl;}

template<class T> class Dijkstra {
public:
    int N;
    T inf;
    vector<T> cost;
    vector<vector<pair<T, int>>> edge;
    
    Dijkstra(const int N, T inf) : N(N), inf(inf),cost(N), edge(N) {
    }
    
    void make_edge(int from, int to, T w) {
        edge[from].push_back({ w,to });
    }
    
    void solve(int start) {
        for(int i = 0; i < N; ++i) cost[i] = inf;
        
        priority_queue<pair<T, int>, vector<pair<T, int>>, greater<pair<T, int>>> pq;
        cost[start] = 0;
        pq.push({ 0,start });
        
        while (!pq.empty()) {
            T v = pq.top().first;
            int from = pq.top().second;
            pq.pop();
            for (auto u : edge[from]) {
                T w = v + u.first;
                int to = u.second;
                if (w < cost[to]) {
                    cost[to] = w;
                    pq.push({ w,to });
                }
            }
        }
        return;
    }
};

int main() {
    while(1){
        ll c,n,m,s,d;
        cin >> c >> n >> m >> s >> d;
        if(c==0){
            return 0;
        }
        s--,d--;
        Dijkstra<ll> dijk((c+1)*n,LOWINF);
        for(int i = 0; i < m; ++i){
            int a,b; cin >> a >> b;
            a--,b--;
            ll w; cin >> w;
            for(int i = 0; i < c; ++i){
                dijk.make_edge(i*n+a, (i+1)*n+b, w/2);
                dijk.make_edge(i*n+b, (i+1)*n+a, w/2);
            }
            for(int i = 0; i <= c; ++i){
                dijk.make_edge(i*n+a, i*n+b, w);
                dijk.make_edge(i*n+b, i*n+a, w);
            }
        }
        dijk.solve(s);
        ll ans = LOWINF;
        for(int i = 0; i <= c; ++i) chmin(ans,dijk.cost[i*n+d]);
        cout << ans << endl;
    }
}

