#include <iostream>
#include <tuple>
#include <vector>
#include <queue> //priority queue
#include <utility> //pair
using namespace std;
#define maxn 200006
#define INF 12334857394875ll
#define pii pair<long long,long long>
long long dis1[maxn];
long long dis2[maxn];
vector<pii> G1[maxn];
vector<pii> G2[maxn];

int t;
long long n, m; // n nodes and m edges
int a, b;//travel from a to b
long long c, d, e; // it takes e to go from c to d

void dijk1(long long n) {
    for (int i=0;i<=n;++i) {
        dis1[i] = INF;
    }
    dis1[a] = 0; //從誰開始
    priority_queue< pii, vector<pii>, greater<pii> > pq;
    pq.push(make_pair(dis1[a],a));
    while (!pq.empty()) {
        pii p = pq.top();
        pq.pop();
        long long disid = p.first;
        long long id = p.second;
        if (dis1[id] != disid) continue;  // 如果新丟出來的單行道並不是最優的一條，就不討論它
        for (pii q:G1[id]) {
            long long to = q.first;
            long long wei = q.second;
            if (dis1[to] > disid + wei) {
                dis1[to] = disid + wei;
                pq.push(make_pair(dis1[to],to));
            }
        }
    }
}


void dijk2(long long n) {
    for (int i=0;i<=n;++i) {
        dis2[i] = INF;
    }
    dis2[b] = 0; //從誰開始
    priority_queue< pii, vector<pii>, greater<pii> > pq;
    pq.push(make_pair(dis2[b],b));
    while (!pq.empty()) {
        pii p = pq.top();
        pq.pop();
        long long disid = p.first;
        long long id = p.second;
        if (dis2[id] != disid) continue;
        for (pii q:G2[id]) {
            long long to = q.first;
            long long wei = q.second;
            if (dis2[to] > disid + wei) {
                dis2[to] = disid + wei;
                pq.push(make_pair(dis2[to],to));
            }
        }
    }
}
long long aa[maxn], ab[maxn], ac[maxn];

int main() {
    ios::sync_with_stdio(0); cin.tie(0);
    cin >> t;
    for(int i=0; i<t; ++i){
        for(int i=0; i<n; i++){
            G1[i].clear();
            G2[i].clear();
        }
        cin >> n>> m >> a >> b;

        for(int i=0; i<m; ++i){
            cin >> c >> d>> e;
//            x --> y, weight = z
//            G[x].push_back(make_pair(y,z));
            G1[c].push_back(make_pair(d,e));
            G2[d].push_back(make_pair(c,e));

            aa[i]=c;
            ab[i]=d;
            ac[i]=e;

//            vector<tuple<int, int, int>> edges;
//            tuple<int, int, int> edge = make_tuple(e, c, d);
//            edges.push_back(edge);
        }
        dijk1(n);
        dijk2(n);

        long long min=INF;
        long long length;
//        bool ok;
        for(int i =0; i<m; i++){
            length=dis1[aa[i]]+dis2[ab[i]]+ac[i];
            if(length!=dis1[b]){
                if(length<min) min=length;
            }
        }
        cout << (min-dis1[b]) << endl;
    }
}


/*
#define INF 12334857394875ll
#define pii pair<int,int> pii;
long long dis[maxn];
vector<pii> G[maxn];

//x --> y, weight = z
//G[x].push_back(make_pair(y,z));

void dijk(int n) {
    for (int i=0;i<n;++i) {
        dis[i] = INF;
    }
    dis[0] = 0;
    prioirity_queue< pii, vector<pii>, greater<pii> > pq;
    pq.push(make_pair(dis[0],0));
    while (!pq.empty()) {
        pii p = pq.top();
        pq.pop();
        int disid = p.first;
        int id = p.second;
        for (pii q:G[id]) {
            int to = q.first;
            int wei = q.second;
            if (dis[to] > disid + wei) {
                dis[to] = disid + wei;
                pq.push(make_pair(dis[to],to));
            }
        }
    }
}*/