#include<bits/stdc++.h>

using namespace std;

#define all(x) (x).begin(), (x).end()
#define sz(x) (int)(x).size()

using ll = long long;

const int N = 1e5 + 5;
const int lovv66 = 228;
vector<int> gr[N];
int used[N];
int d[N], need, p[N];
vector<int> ans;
mt19937 gen;

void bfs(int st) {
    d[st] = 0;
    p[st] = -1;
    queue<int> q;
    q.push(st);
    while (!q.empty()) {
        int v = q.front();
        q.pop();
        for (int u: gr[v]) {
            if (used[u] == 1 || d[u] <= d[v] + 1)
                continue;
            p[u] = v;
            d[u] = d[v] + 1;
            q.push(u);
        }
    }
}

int mx(const vector<int> &ar) {
    pair<int, int> best = {0, 0};
    for (int i: ar) {
        best = max(best, {d[i], i});
    }
    return best.second;
}

void sol(vector<int> &ar) {
    if (ar.empty())
        return;
    for (int u: ar) {
        d[u] = N;
    }
    int st = ar[gen() % sz(ar)];
    bfs(st);
    int st1 = mx(ar);
    for (int u: ar) {
        d[u] = N;
    }
    bfs(st1);
    vector<int> way;
    int mx1 = mx(ar);
    while (mx1 != -1) {
        way.push_back(mx1);
        mx1 = p[mx1];
    }
    for (int u: ar) {
        d[u] = N;
    }
    queue<int> q;
    for (int i = 0; i < sz(ar);) {
        ans.push_back(ar[i] + 1);
        d[ar[i]] = 0;
        q.push(ar[i]);
        int next = need * 2 + 1;
        if (next + i >= sz(ar)) {
            if (need + 1 + i < sz(ar)) {
                i = need + 1 + i;
            } else {
                break;
            }
        } else {
            i += next;
        }
    }
    while (!q.empty()) {
        int v = q.front();
        q.pop();
        for (int u: gr[v]) {
            if (used[u] == 1 || d[u] <= d[v] + 1)
                continue;
            d[u] = d[v] + 1;
            q.push(u);
        }
    }
    vector<int> ar1;
    while (!ar.empty()) {
        int i = ar.back();
        if (d[i] <= need) {
            used[i] = 1;
        } else {
            ar1.push_back(i);
        }
        ar.pop_back();
    }
    sol(ar1);
}

void solve() {
    int n, m;
    cin >> n >> m;
    for (int i = 0; i < n; i++) {
        gr[i].clear();
        used[i] = 0;
    }
    ans.clear();
    for (int i = 0; i < m; i++) {
        int u, v;
        cin >> u >> v;
        v--, u--;
        gr[u].push_back(v);
        gr[v].push_back(u);
    }

    vector<int> ar(n);
    iota(all(ar), 0);
    need = ceil(sqrt(n));

    sol(ar);

    if (sz(ans) > need) {
        assert(false);
        cout << "-1\n";
    } else {
        cout << sz(ans) << '\n';
        for (int i: ans) {
            cout << i << ' ';
        }
        cout << '\n';
    }
}

int main() {
#ifndef LOCAL
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
#else
    freopen("input.txt", "r", stdin);
#endif
    gen.seed(lovv66);
    int t;
    cin >> t;
    while (t--)
        solve();
    return 0;
}