#include "iostream"
#include "queue"
using namespace std;
#define N 10000
#define Max 0x7FFFFFFF
typedef struct Node{
    int u, value, next;
}node;
node e[N];
int n, m;
int dis[N], p[N];
bool vis[N];
void init(){
    memset(p, -1, sizeof(p));
    memset(vis, false, sizeof(vis));
    fill(dis, dis+N, Max);
    int temp = 0; 
    int a, b, c;
    for(int i=0; i<n; i++){
        cin>>a>>b>>c;
        e[temp].u = b;
        e[temp].value = c;
        e[temp].next = p[a];
        p[a] = temp;
        temp ++;
        e[temp].u = a;
        e[temp].value = c;
        e[temp].next = p[b];
        p[b] = temp;
        temp++;
    }
}
void spfa(int s){
    dis[s] = 0;
    queue<int> q;
    q.push(s);
    while(!q.empty()){
        int t = q.front();
        q.pop();
        vis[t] = false;
        int j;
        for(j=p[t]; j!=-1; j=e[j].next){
            int w=e[j].value;
            int temp = e[j].u;
            if(w+dis[t] < dis[temp]){
                dis[temp] = w+dis[t];
                if(!vis[temp]){
                    vis[temp] = true;
                    q.push(temp);
                }
            }
        }
    }
}
int main()
{
    while(cin>>n>>m && (n+m))
    {
        init();
        spfa(1);
        cout<<dis[m]<<endl;
    }
    return 0;
}