#include <stdio.h>
int Ways[50002];
long Count[10002], Next[10002], Cost[50002];
long pomField[10002][3];
long Value[10002], N, Begin, End, pom, ind, pom1, pom2, Roads, Max;
short int Temp[10002], Found;

int main(){
  Max=60000000;
  scanf("%ld%ld%ld%ld",&N,&Roads,&Begin,&End);
  while((N!=0) && (Roads!=0) && (Begin!=0) && (End!=0)) {
  for (pom=1; pom<=N; pom++) {
    Value[pom]=Max;
    Temp[pom]=1;
    Count[pom]=0;
  }
  for (pom=1; pom<=Roads; pom++) {
    scanf("%ld%ld%ld",&pomField[pom][0],&pomField[pom][1],&pomField[pom][2]);
    Count[pomField[pom][0]]+=1;
  }    
  ind=1;
  for(pom=1; pom<=N; pom++) {
    pom1=1;
    pom2=0;
    while (pom2<Count[pom]) {
      if(pomField[pom1][0]==pom) {
        Ways[ind]=pomField[pom1][1];
	Cost[ind]=pomField[pom1][2];
	pom2++;
	ind++;
      }
      pom1++;
    }
  }
  Next[0]=0;
  Next[1]=1;
  for(pom=1; pom<=N; pom++) Next[pom+1]=Next[pom]+Count[pom];
  Value[Begin]=0;
  Found=0;
  while (Temp[End]==1) {
    pom1=End;
    for(pom2=1; pom2<=N; pom2++) 
      if((Temp[pom2]) && (Value[pom2] < Value[pom1])) pom1=pom2;
    Temp[pom1]=0;
    for(pom2=Next[pom1]; pom2<Next[pom1+1]; pom2++) {
      if(Value[pom1]+Cost[pom2] < Value[Ways[pom2]]) 
        Value[Ways[pom2]] = Value[pom1]+Cost[pom2];
    }
  }
  printf("%ld\n",Value[End]);
  scanf("%ld%ld%ld%ld",&N,&Roads,&Begin,&End);
  }
  return 0;
}