#include <bits/stdc++.h>
using namespace std;

#define FOR(i, a, b) for(int i = (a); i < (b); ++i)
#define REP(i, n) FOR(i, 0, n)
#define _ << " " <<

typedef long long ll;
typedef pair<int, int> point;

const int MAXN = 100005;

int test, n, m, a, b, c, poc, kraj;
int dist[MAXN], bio[MAXN];
priority_queue <point> Q;

void dijkstra(){
    vector <point> edge[MAXN];
    memset(bio, 0, sizeof(bio));
    memset(dist, 0, sizeof(dist));
    int d, cvor;

    REP(i, m){
        cin >> a >> b >> c;
        edge[a].push_back(point(b, c));
        edge[b].push_back(point(a, c));
    }

    Q.push(point(0, poc));
    while(!Q.empty()){
        while(!Q.empty() && bio[Q.top().second]) Q.pop();
        if(Q.empty()) break;
        cvor = Q.top().second;
        d = -Q.top().first;
        Q.pop();

        bio[cvor] = 1;
        dist[cvor] = d;

        REP(i, edge[cvor].size()){
            int ncvor = edge[cvor][i].first;
            if(bio[ncvor]) continue;
            Q.push(point(-(d + edge[cvor][i].second), ncvor));
        }
    }
    if(poc == kraj)
        cout << 0;
    else{
        if(dist[kraj] == 0)
            cout << "NONE";
        else
            cout << dist[kraj];
    }
    cout << "\n";
}

int main(){
    ios_base::sync_with_stdio(false);
    cin >> test;
    REP(i, test){
        cin >> n >> m >> poc >> kraj;
        dijkstra();
    }
return 0;
}