anfjsfla

#include <bits/stdc++.h>
using namespace std;
#define fr(i, a, b) for(int i = a, _ = b; i < _; i++)
#define mp make_pair
#define pb push_back
typedef long long ll;
typedef pair<int, int> pii;
#define F first
#define S second

int djk(vector<pii> adj[], int begin, int dest, int n){
    int dist[n+1];
    fr(i, 0, n+1)
        dist[i] = INT_MAX;

    dist[begin] = 0;
    priority_queue<pii, vector<pii>, greater<pii> > pq;
    pq.push(mp(dist[begin], begin));
    while(!pq.empty()){
        int node = pq.top().S;
        pq.pop();
        for(pii v : adj[node])
            if(dist[node] + v.F < dist[v.S]){
                dist[v.S] = dist[node] + v.F;
                pq.push(mp(dist[v.S], v.S));
            }
    }

    return dist[dest];
}

int main(){
    int nn;
    scanf("%d" ,&nn);
    fr(lo, 0, nn){
        int n, m, begin, dest, v, w, c;
        scanf("%d%d%d%d" ,&n, &m, &begin, &dest);
        vector<pii> adj[n+1];
        fr(i, 0, m){
            scanf("%d%d%d" ,&v ,&w, &c);
            adj[v].pb(mp(c, w));
            adj[w].pb(mp(c, v));
        }

        int k = djk(adj, begin, dest, n);
        if(k == INT_MAX)
            cout << "NONE" << endl;
        else
            cout << k << endl;
    }
    return 0;
}