/*
 * HIGHWAYS.cpp
 *
 *  Created on: Jun 19, 2014
 *      Author: Arpit Bhayani
 */

#include <queue>
#include <climits>
#include <cstdio>
#include <cstdlib>
#include <iostream>

using namespace std;

#define DEBUG 0
#define gc getchar
#define ll long long

void scanint(ll int &x) {
    register ll int c = gc();
    x = 0;
    for (; (c < 48 || c > 57); c = gc())
        ;
    for (; c > 47 && c < 58; c = gc()) {
        x = (x << 1) + (x << 3) + c - 48;
    }
}

int readline(char * str) {

    int i = 0;
    char ch;
    while ((ch = getchar()) != '\n') {
        str[i++] = ch;
    }
    str[i] = '\0';
    return i;
}

#define SIZE 100001

int dist[SIZE];

struct edge {
    int v;
    int w;
};


bool operator <(struct edge a, struct edge b) {
    return a.w < b.w;
}

vector<edge> node[SIZE];

int main(int argc, char * argv[]) {

    int t;
    scanf("%d", &t);
    while (t--) {

        priority_queue< edge > q;

        int n, m, s, e;

        scanf("%d%d%d%d", &n, &m, &s, &e);

        for (int i = 1; i <= n; i++) {
            node[i].clear();
            dist[i] = INT_MAX;
        }

        for (int i = 0; i < m; i++) {
            int a, b, w;
            scanf("%d%d%d", &a, &b, &w);
            node[a].push_back((edge ) { b, w });
            node[b].push_back((edge ) { a, w });
        }

        dist[s] = 0;
        q.push((edge ) { s, 0 });

        while (!q.empty()) {
            edge p = q.top();
            q.pop();

            for (int i = 0; i < node[p.v].size(); i++) {
                edge k = node[p.v][i];
                if (dist[p.v] + k.w < dist[k.v]) {
                    dist[k.v] = dist[p.v] + k.w;
                    q.push(k);
                }
            }
        }

        if (dist[e] == INT_MAX) {
            printf("NONE\n");
        } else {
            printf("%d\n", dist[e]);
        }

    }
    return 0;
}