#include <iostream>
#include <iomanip>
#include <cstdio>
#include <string>
#include <cstring>
#include <deque>
#include <list>
#include <queue>
#include <stack>
#include <vector>
#include <utility>
#include <algorithm>
#include <map>
#include <set>
#include <complex>
#include <cmath>
#include <limits>
#include <cfloat>
#include <climits>
#include <ctime>
#include <cassert>
#include <numeric>
#include <fstream>
#include <functional>
#include <bitset>

using namespace std;
#define int long long int
const int INF = 1001001001001001LL;

int di[] = {-1, 0, 1, 0, -1, 1, 1, -1};
int dj[] = {0, 1, 0, -1, 1, 1, -1, -1};

vector<int> dijk(int s, int v, vector<vector<pair<int, int>>> adjlist){
    priority_queue <pair<int, int>> wait;
    vector<int> result(v, INF);

    result[s] = 0;
    wait.push(make_pair(0,s));

    while(!wait.empty()){
        int nowpoint = wait.top().second;
        int nowcost = -wait.top().first;
        wait.pop();

        if(result[nowpoint] < nowcost) continue;

        for(int i = 0; i < adjlist[nowpoint].size(); i++){
            int nextpoint = adjlist[nowpoint][i].second;
            int nextcost = nowcost + adjlist[nowpoint][i].first;
            if(result[nextpoint] > nextcost){
                result[nextpoint] = nextcost;
                wait.push(make_pair(-nextcost, nextpoint));
            }
        }
    }
    return result;
}



signed main(){
    

    while(1){
    int c, n, m, s, t; cin >> c >> n >> m >> s >> t;
    s--;
    t--;
    if(!n) break;
    vector<vector<int> > toNode(n, vector<int> (c + 1));
    int num = 0;
    for(int i = 0; i < n; i++){
        for(int j = 0; j <= c; j++){
            toNode[i][j] = num;
            num++;
        }
    }

    vector<vector<pair<int, int>>> adj(num);

    for(int i = 0; i < m; i++){
        int a, b, f; cin >> a >> b >> f;
        a--;
        b--;

        for(int iii = 0; iii < 2; iii++){

            for(int j = 0; j <= c; j++){
                    
                int cur = toNode[a][j];
                // 使わない
                int nxt = toNode[b][j];
                adj[cur].push_back({f, nxt});
                
                nxt = toNode[b][j + 1];
                // 使う
                if(j != c){
                    adj[cur].push_back({f / 2, nxt});
                }
            }
            swap(a, b);
        }
    }

    
    int ans = INF;
    int S = toNode[s][0];
    vector<int> result = dijk(S, num, adj);
    for(int j = 0; j <= c; j++){
        int G = toNode[t][j];
        ans = min(ans, result[G]);
    }

    cout << ans << endl;
    }
    return 0;
}

