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

#define MAX 1000000000

int a[10001],v[10002],h[100001][3],b[10001],c[10001],d[10001];
int n,m,o,x,y,i,j,k,l;

int cmp(const void *a, const void *b)
{
  return *(int *)a - *(int *)b;
}

void Swap(int i,int j)
{
  int k;
  k = a[i];
  a[i] = a[j];
  a[j] = k;
  d[a[i]] = i;
  d[a[j]] = j;
}

void Update(int i)
{
  int j;
  i = d[i];
  while (i > 1)
  {
    j = i/2;
    if (b[a[j]] <= b[a[i]])
      break;
    Swap(i, j);
    i = j;
  }
}

int main()
{
  while(1)
  {
    scanf("%d %d %d %d\n", &n, &m, &x, &y);

    if (n == 0)
      break;

    for (i=1; i<=m; i++)
    {
      scanf("%d %d %d\n", &j, &k, &l);
      h[2*i-1][0] = j;
      h[2*i-1][1] = k;
      h[2*i-1][2] = l;
      h[2*i][0] = k;
      h[2*i][1] = j;
      h[2*i][2] = l;
    }
    m*=2;

    qsort(&h[1], m, sizeof(int) * 3, cmp);

    j = 1;
    for (i=1; i<=n; i++)
    {
      v[i] = j;
      while (j<=m && h[j][0] <= i)
	j++;
    }
    v[n+1] = j;
    o = n;

    /*for (i=1; i<=n; i++)
    {
      printf("%d: ", i);
      for (j=v[i]; j<v[i+1]; j++)
	printf("%d ", h[j][1]);
      printf("\n");
    }*/

    for (i=1; i<=n; i++)
    {
      a[i] = i;
      d[i] = i;
      b[i] = MAX;
      c[i] = 1;
    }
    b[x] = 0;
    Update(x);
    

    while (c[y])
    {
      i = a[1];
      c[i] = 0;


      a[1] = a[o--];
      j = 1;
      while (1)
      {
	k = j+j;
	if (k>o)
	  break;
	if (k<o && b[a[k]]>b[a[k+1]])
	  k++;
	if (b[a[j]]<=b[a[k]])
	  break;
	Swap(j, k);
	j = k;
      }
      
      for (k=v[i]; k<v[i+1]; k++)
      {
	j = h[k][1];
	l = b[i] + h[k][2];
	if (l < b[j])
	{
	  b[j] = l;
	  Update(j);
	}
      }
    }

    printf("%d\n", b[y]);
    
  }
  
  return 0;
}