#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;

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; fr = 1;
    while (fr) {
      //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]; }
      }
      //      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) done[j.v] = 1; fr++;
	}
      }
      done[ak] = 2;
      fr--;
    }
    cout << d[c]<<endl;
  }

  return 0;
}