#include <bits/stdc++.h>

using namespace std;

#define IMPOSSIVEL 0x3f3f3f3f

int best[500];
bool visited[500];
int n;

int matriz[500][500];
int matrizT[500][500];

void dijkstra(int s) {
    memset(best, 0x3f, sizeof(best));
    memset(visited, false, sizeof(visited));

    best[s] = 0;
    while (true) {
        int x = -1, menor = IMPOSSIVEL;
        for (int k = 0; k < n; k++) {
            if (best[k] < menor && !visited[k]) {
                x = k;
                menor = best[x];
            }
        }
        if(x == -1) break;
        // cout << "next " << x << " - " << best[x] << endl;
        visited[x] = true;

        for (int i = 0; i < n; i++) {
            if (matriz[x][i] == 0)
                continue;
            if (best[x] + matriz[x][i] < best[i]) {
                best[i] = best[x] + matriz[x][i];
            }
        }
    }
}

void dfs(int u) {
    visited[u] = true;
    for (int i = 0; i< n; i++) {
        if (matrizT[u][i] == 0)
                continue;
        if (best[i] == best[u] - matrizT[u][i]) {
            matriz[i][u] = 0;
            if (!visited[i])
                dfs(i);
        }
    }
}


int main(int argc, char const *argv[])
{
    for (;;) {
        int m;
        cin >> n >> m;
        if (n == 0 && m == 0)
            break;

        int s, d;
        cin >> s >> d;

        memset(matriz, 0, sizeof(matriz));
        memset(matrizT, 0, sizeof(matrizT));
        for(int i = 0; i < m; i++) {
            int u,v,p;
            cin >> u >> v >> p;
            matriz[u][v] = p;
            matrizT[v][u] = p;
        }

        dijkstra(s);
        if (best[d] == IMPOSSIVEL) {
            cout << "-1" << endl;
            return 0;
        }

        memset(visited, false, sizeof(visited));
        visited[s] = true;
        dfs(d);
        dijkstra(s);
        if (best[d] == IMPOSSIVEL)
            cout << "-1" << endl;
        else
            cout << best[d] << endl;
    }

    return 0;
}