#include <iostream>
#include <stack>

#define maxn 10000
#define moc -1

struct dv {
  int v, c;
};

int n,m,s,c;
stack<dv> adj[maxn];
int d[maxn];
int done[maxn];


int fr[maxn];
int fb, fe;

int popni() {
  fb++;
  return fr[fb-1];
}

void zrus(int koho) {
  int akt=fb;
  while (fr[akt] != koho) akt++;
  while (akt<n) {fr[akt] = fr[akt+1]; akt++;}
  fe--;
}

void pridej(int koho) {
  int akt =fb;
  while (d[fr[akt]] < d[koho] && akt<fe) akt++;
  int uloz = akt;
  fe++;
  akt = fe;
  while (akt > uloz) {fr[akt] = fr[akt-1]; akt--;}
  fr[uloz] = koho;
}

int main() {
  while (1) {

    cin >> n >> m >> s>>c;
    if (n==0 && m==0 && s == 0 && c==0) break;
    s--; c--;
    for (int i=0; i<m; i++) {
      int k, l, j;
      dv pom;//, pom2;
      cin >> k>> l>> j;
      pom.v = l -1;
      pom.c = j;
      //      pom2.v = k-1;
      //      pom2.c = j;
      adj[k-1].push(pom);
      //      adj[l-1].push(pom2);
    }
    for (int i=0; i<n; i++) { d[i]=moc; done[i] = 0;}
    d[s] = 0; done[s] = 1; fb = 0; fe =1; fr[0] = s;
    while (fb != fe) {
      //find smallest of done=1
      /*      int ak, pom = moc;
      for (int i=0; i<n; i++) {
	if (done[i]==1 && d[i] != moc && (pom==moc || d[i]<pom)) {ak = i; pom = d[i]; }
	}*/
      int ak = popni();
      //      cout << "scanning "<<ak<<" "<<d[ak]<<endl;
      //scan:
      dv j;
      while (! adj[ak].empty()) {
	j = adj[ak].top();
	adj[ak].pop();
	//	cout <<"mam" << j.v<<endl;
	if (d[j.v] == moc || d[j.v] > j.c + d[ak]) {
	  d[j.v] = d[ak] + j.c;
	  if (done[j.v] == 0) { pridej(j.v); done[j.v] = 1;}
	  else {zrus(j.v); pridej(j.v);}
	}
      }
      done[ak] = 2;
      if (ak == c) break;
    }
    cout << d[c]<<endl;
  }

  return 0;
}