#include <bits/stdc++.h>
using namespace std;
#define X first
#define Y second
#define rep(i,a,n) for(int i=(a);i<=(n);++i)
#define dep(i,a,n) for(int i=(a);i>=(n);--i)
#define MIN(a,b) (a)=min(a,b)
typedef long long ll;
const int N = 555;
const ll inf = 1ll << 40;
vector<pair<int, ll>>a[N];
int m, n, t, C, s, x, y, S[N], T[N], H, st[N], hu[N], h[N], nu, vi[N], i, q;
ll dp[N], sh[N], pr[N], nt[N], qu[N], pq[N], fa = 0, p[N], z, ts, la, ra, ct, ca, c, d, lx[2][N], ld[2][N];
void dfs(int x, int f, int d) {
    vi[x] = 1;
    st[d] = x;

    for (auto ii : a[x])
        if (ii.X != f) {
            int i = ii.X;

            if (vi[i]) {
                if (!H && (H = 1))
                    dep(k, d, 0) {
                    hu[st[k]] = 1;
                    h[++nu] = st[k];

                    if (st[k] == i)
                        break;
                }
            } else
                dfs(i, x, d + 1);
        }
}
void dh(int x, int f, int fl = 0) {
    sh[x] = inf;
    dp[x] = 0;

    for (auto ii : a[x])
        if (ii.X != f && !(hu[ii.X] && hu[x])) {
            int i = ii.X;
            dh(i, x, fl);
            MIN(sh[x], sh[i] + ii.Y);
            dp[x] += max(0ll, min(dp[i] - ii.Y, sh[i] - ii.Y + 1));
        }

    if (hu[x] && fl)
        dp[x] += fa, MIN(sh[x], ts);

    if (S[x])
        sh[x] = 0;

    if (x == 1)
        sh[x] = inf;

    if (T[x])
        dp[x] = inf;
}
ll cal(ll a, ll br, ll bl, ll cr, ll cl) {
    if (br > cr)
        br -= cr, cr = 0;
    else
        cr -= br, br = 0;

    if (bl > cl)
        bl -= cl, cl = 0;
    else
        cl -= bl, bl = 0;

    return max(0ll, a + br + bl - min(cr, cl));
}
int main() {
    scanf("%d", &C);
    rep(_, 1, C) {
        scanf("%d%d%d%d", &n, &m, &s, &t);
        rep(i, 1, n)a[i].clear();
        rep(i, 1, m)scanf("%d%d%lld", &x, &y, &z), a[x].push_back({y, z + 1}), a[y].push_back({x, z + 1});
        rep(i, 1, n)hu[i] = vi[i] = h[i] = S[i] = T[i] = nu = H = 0;
        fa = inf;
        rep(i, 1, s)scanf("%d", &x), S[x] = 1;
        rep(i, 1, t)scanf("%d", &x), T[x] = 1;
        dfs(1, 0, 0);

        rep(i, 1, n)if (hu[i])
            dh(i, 0);

        h[0] = h[nu];

        rep(i, 0, nu - 1)for (auto ii : a[h[i]])
            if (ii.X == h[i + 1])
                qu[i] = ii.Y;

        pq[0] = 0;
        rep(i, 1, nu)pq[i] = pq[i - 1] + qu[i - 1];
        pr[0] = sh[h[0]];
        rep(i, 1, nu)pr[i] = min(sh[h[i]], pr[i - 1] + qu[i - 1]);
        nt[nu] = sh[h[nu]];
        dep(i, nu - 1, 0)nt[i] = min(sh[h[i]], nt[i + 1] + qu[i]);
        rep(i, 1, nu - 1)p[i] = dp[h[i]];
        p[0] = p[nu] = 0;
        ts = min(pr[nu], nt[0]);

        if (nu)
            for (c = d = 0, i = q = 1; i >= 0; i += q) {
                c += qu[i - (q > 0)];
                lx[q < 0][i] = c - 1;
                ld[q < 0][i] = d;

                if (dp[h[i]] > c)
                    d += dp[h[i]] - c, c = 0;
                else
                    c -= dp[h[i]];

                if (T[h[i]])
                    d = inf;

                if (i == nu)
                    q = -1, c = d = 0;
            }

        //Type A
        if (nu)
            for (la = inf, ct = ca = 0, i = q = 1; i >= 0; i += q) {
                MIN(la, max(0ll, (q > 0 ? nt[i] : pr[i]) - ct - (qu[i - 1 + (q < 0)] - 1)) + ca);
                ct += qu[i - (q > 0)];

                if (dp[h[i]] > ct)
                    ca += dp[h[i]] - ct, ct = 0;
                else
                    ct -= dp[h[i]];

                if (i == nu)
                    q = -1, ct = ca = 0, ra = la, la = inf;
            }

        MIN(fa, la + ra);
        //Type B
        rep(i, 1, nu - 1)rep(j, i, nu - 1)rep(k, i, j)
        MIN(fa, ld[0][i] + ld[1][j] + cal(sh[h[k]], pq[j] - pq[k], pq[k] - pq[i], lx[1][j], lx[0][i]));

        //Type C
        if (nu)
            for (ca = ct = 0, i = q = 1; i >= 0; i += q) {
                ct += qu[i - (q > 0)];

                if (p[i] > ct)
                    ca += p[i] - ct, p[i] = ct, ct = 0;
                else
                    ct -= p[i];

                if (i == nu)
                    q = -1, ct = 0;
            }

        MIN(fa, ca);

        dh(1, 0, 1);
        printf("%lld\n", min(1000000ll, dp[1]));
    }
    return 0;
}