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

#define NEK 1000000000

int d[10002];
int p[10002];

int hash[11000];

struct tab {
	int uod, udo, del;
} tb[50002];


int N,M,S,C;

int fronta[1000000];
int frbeg, frend;

void init_queue(void) {
	frbeg = frend = 0;
}

void enqueue(int u) {
	fronta[frend] = u;
	frend = (frend+1) % 1000000;
}

int dequeue(void) {
	int x = fronta[frbeg];
	frbeg = (frbeg+1) % 1000000;
	return x;
}
bool isempty(void) {
	return frend==frbeg;
}

int w(int, int);

void relax_q(int u, int v) {
	int ww = w(u,v);
	if( d[v] > (d[u] + ww) ) {
		d[v] = d[u] + ww;
		p[v] = u;
		enqueue(v);
	}
}

int w(int u, int v) {
	int i = hash[u];
	while( (tb[i].uod == u) && (tb[i].udo != v) ) i++;
	return (tb[i].udo == v) ? tb[i].del : NEK;
}

void init_paths(void) {
	for(int i=0; i<=N; i++) {
		d[i] = NEK;
		p[i] = 0;
	}
	d[S] = 0;
}

void relax(int u, int v) {
	if( d[v] > (d[u]+w(u,v)) ) {
		d[v] = d[u] + w(u,v);
		p[v] = u;
	}
}

void makehash(void) {
	for(int i = M; i>0; i--) {
		hash[tb[i].uod] = i;
	}
}

int cmp(const void *a, const void *b) {
	if( ((tab*)a)->uod < ((tab*)b)->uod) return -1;
	if( ((tab*)a)->uod == ((tab*)b)->uod) return 0;
	return 1;
}

int main(void) {
	do {
		scanf("%d %d %d %d", &N, &M, &S, &C);
		if( (N | M | S | C) == 0 ) return 0;

		for(int	i=1; i<=M; i++) {
			scanf("%d %d %d", &tb[i].uod, &tb[i].udo, &tb[i].del);
		}
	
		//sort
		qsort(&tb[1], M, sizeof(tab), cmp);

		//make hash
		makehash();
	
		//b-f
		init_paths();
		init_queue();
		enqueue(S);
		
		int u,z;
		
		while( !isempty() ) {
			u = dequeue();
			z = hash[u];
			while(tb[z].uod == u) {
				relax_q(u,tb[z].udo);
				z++;
			}
		}
		
		printf("%d\n",d[C]);
	} while (1);
}