#include <bits/stdc++.h>

#define INF 0x7FFFFFFF
using namespace std;

using ll = long long;
using pll = pair<ll, ll>;
using graph = vector<vector<pll>>;
const int MAXN = 510;

vector<ll> dijk(int x, graph& g) {
    priority_queue<pll> pq;
    pq.push({0, x});
    vector<ll> dist(MAXN, INF);
    while (pq.size()){
        auto [w, v] = pq.top();
        pq.pop();
        w = -w;
        if (dist[v] <= w) continue;
        dist[v] = w;
        for (auto [u, ww] : g[v]) {
            if (dist[u] <= w + ww) continue;
            pq.push({-(w+ww), u});
        }
    }
    return dist;
}

ll almost_dijk(int s, int d, graph& g, vector<ll>& dist_s, vector<ll>& dist_d) {
    ll best = dist_s[d];
    if (best == INF) return -1;

    priority_queue<pll> pq;
    pq.push({0, s});
    vector<ll> dist(MAXN, INF);
    while (pq.size()){
        auto [w, v] = pq.top();
        pq.pop();
        w = -w;
        if (v == d) return w;
        if (dist[v] <= w) continue;
        dist[v] = w;
        for (auto [u, ww] : g[v]) {
            if (dist_s[v] + ww + dist_d[u] <= best) continue; // pula essa aresta, corresponde a um caminho minimo
            if (dist[u] <= w + ww) continue;
            pq.push({-(w+ww), u});
        }
    }
    return -1;
}

int main(){
    ios::sync_with_stdio(0);
    cin.tie(0); cout.tie(0);

    int n, m; 
    while (cin>>n>>m, n!=0 && m!=0){
        int s, d; cin >> s >> d;
        vector<vector<pll>> g(MAXN);
        vector<vector<pll>> g_rev(MAXN);
        for (int i=0;i<m;i++){
            int u,v,p; cin >> u >> v >> p;
            g[u].push_back({v, p});
            g_rev[v].push_back({u, p});
        }
        vector<ll> dist_s = dijk(s, g);
        vector<ll> dist_d = dijk(d, g_rev);
        cout << almost_dijk(s, d, g, dist_s, dist_d) << '\n';
    }
}