#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
#include <cstdlib>
#include <queue>
using namespace std;

typedef long long ll;
const int N = 105;
const int INF = 0x3f3f3f3f;
int n, m;
int s, t, K;
int h[N]; 
bool vis[N];
struct Node {
    int to, dis;
};
int gra[N][N], gra2[N][N];

bool operator < (const Node& a, const Node& b) {
    return (a.dis + h[a.to] > b.dis + h[b.to]);
}

void init() {
    memset(vis, 0, sizeof(vis));
    for(int i = 0; i <= n + 1; i++) h[i] = INF;
    h[t] = 0;
    for(int i = 1; i <= n; i++) {
        int x, m = INF;
        for(int j = 1; j <= n; j++) {
            if(!vis[j] && m > h[j]) {
                m = h[j];   
                x = j;
            }
        }
        vis[x] = true;
        for (int j = 1; j <= n; j++) {
            if (!vis[j] && gra2[x][j] + h[x] < h[j]) {
                h[j] = gra2[x][j] + h[x];
            }   
        }
    }
}

int Astar() {
    priority_queue<Node> Q;
    init();
    if (s == t) K++;
    if (h[s] == INF) return -1;
    int ans = -1, count = 0;
    Node p;
    p.to = s;
    p.dis = 0;
    Q.push(p);
    while(!Q.empty()) {
        p = Q.top(); Q.pop();
        if (p.to == t) count++;
        if (count == K) {
            ans = p.dis;    
            break;
        }
        for (int i = 1; i <= n; i++) {
            if (gra[p.to][i] != INF) {
                Q.push((Node){i, p.dis + gra[p.to][i]});    
            }   
        }
    }
    return ans;
}

void input() {
    for (int i = 0; i <= n; i++) {
        for (int j = 0; j <= n; j++) {
            gra[i][j] = INF;    
            gra2[i][j] = INF;
        }
    }
    scanf("%d %d %d", &s, &t, &K);
    int u, v, d;
    for (int i = 0; i < m; i++) {
        scanf("%d %d %d", &u, &v, &d);
        gra[u][v] = min(gra[u][v], d);
        gra2[v][u] = min(gra2[v][u], d);
    }
}

int main() {
    while (scanf("%d %d", &n, &m) == 2) {
        if (n == 0 && m == 0) break;
        input();    
        printf("%d\n", Astar());
    }
    return 0;
}

#include<cstdio>  
#include<algorithm>  
#include<vector>  
#include<cstring>  
#include<stack>  
#include<iostream>  
#include<queue>  
using namespace std;  
const int N = 105;  
int n, m;  
int s, t, k;  
struct Edge{  
    int to, dis;  
};  
vector<Edge> G[N];  
int vis[N];  

int BFS(){  
    int ans = -1;
    priority_queue<pair<int, int> > q;  
    memset(vis, 0, sizeof vis);  
    q.push(make_pair(0, s));  
    while(!q.empty()){  
        pair<int, int> p = q.top();  
        q.pop();  
        int dist = -p.first;  
        int pos = p.second;  
        if(vis[pos] > k) continue;  
        vis[pos]++;  
        if(pos == t && vis[pos] == k){  
            ans = dist;  
            break;
        }  
        for(int i = 0;i < G[pos].size();i++){  
            int to = G[pos][i].to;  
            int dis = G[pos][i].dis;  
            q.push(make_pair(-(dis + dist), to));  
        }  
    }  
    return ans;
}  

int main(){  
    while(scanf("%d%d", &n, &m)){  
        if(n == 0 && m == 0) break;  
        scanf("%d%d%d", &s, &t, &k);  
        for(int i = 0; i <= n; i++) G[i].clear();  
        for (int i = 0; i < m; i++) {
            int u, v, d;  
            scanf("%d%d%d", &u, &v, &d);  
            G[u].push_back((Edge){v, d});  
        }  
        printf("%d\n", BFS());  
    }  
    return 0;  
}