#include <limits.h>
#include <stdio.h>
#include <stdlib.h>

#define MAXN 16384
#define MAXM 65536

struct vert
{
  unsigned num_arcs, na;
  struct arc **arcs;
  unsigned dist;
  char done;
};

static struct vert verts[MAXN];

struct arc
{
  unsigned f, t, v;
} arcs[MAXM];

int
main (void)
{
  for (;;)
    {
      unsigned n, m, s, c;
      struct vert *v;
      struct arc *a;

      scanf ("%u%u%u%u", &n, &m, &s, &c);
      if (n == 0 && m == 0 && s == 0 && c == 0)
	break;
      for (a = arcs; a < arcs + m; a++)
	{
	  scanf ("%u%u%u", &a->f, &a->t, &a->v);
	  a->f--;
	  a->t--;
	  verts[a->f].na++;
	}
      for (v = verts; v < verts + n; v++)
	{
	  v->arcs = realloc (v->arcs, sizeof (*v->arcs) * v->na);
	  v->dist = UINT_MAX;
	  v->num_arcs = 0;
	  v->done = 0;
	}
      for (a = arcs; a < arcs + m; a++)
	{
	  v = verts + a->f;
	  v->arcs[v->num_arcs++] = a;
	}
      verts[s - 1].dist = 0;
      while (verts[c - 1].done == 0)
	{
	  struct vert *max;
	  struct arc **ap;

	  max = NULL;
	  for (v = verts; v < verts + n; v++)
	    {
	      if (v->done == 0 && (max == NULL
				   || max->dist > v->dist))
		max = v;
	    }
	  v = max;
	  v->done = 1;
	  for (ap = v->arcs; ap < v->arcs + v->num_arcs; ap++)
	    {
	      struct vert *v2;
	      unsigned val;

	      v2 = verts + (*ap)->t;
	      val = (*ap)->v + v->dist;
	      if (v2->dist > val)
		v2->dist = val;
	    }
	}
      printf ("%u\n", verts[c - 1].dist);
    }
  return EXIT_SUCCESS;
}