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

void dfs(int v, vector <vector <int> > &g, vector <bool> &u, vector <int> &p, vector <int> &dp) {
  u[v] = 1;
  for (int to: g[v]) {
    if (u[to]) {
      continue;
    }
    p[to] = v;
    dfs(to, g, u, p, dp);
    dp[v] = max(dp[v], dp[to] + 1);
  }
}

void dfs2(int v, vector <vector <int> > &g, vector <bool> &u, vector <int> &p, vector <int> &dp, vector <int> &dp_up) {
  u[v] = 1;
  if (p[v] != -1) {
    int u = p[v];
    dp_up[v] = dp_up[u] + 1;
    for (int to: g[u]) {
      if (p[u] != to && to != v) {
        dp_up[v] = max(dp_up[v], dp[to] + 2);
      }
    }
  }
  for (int to: g[v]) {
    if (!u[to]) {
      dfs2(to, g, u, p, dp, dp_up);
    }
  }
}
const int M = 1e9 + 7;
void solve() {
  int n;
  cin >> n;
  vector <vector <int> > g(n);
  for (int i = 1; i < n; ++i) {
    int x, y;
    cin >> x >> y;
    --x, --y;
    g[x].push_back(y);
    g[y].push_back(x);
  }
  for (int i = 0; i < n; ++i) {
    if (g[i].size() > 3) {
      cout << -1 << endl;
      return;
    }
  }
  vector <int> dp(n), p(n, -1);
  vector <bool> u(n);
  dfs(0, g, u, p, dp);
  vector <int> dp_up(n);
  u.assign(n, 0);
  dfs2(0, g, u, p, dp, dp_up);
  int ans_h = 1000000000, ans_v = -1;
  for (int i = 0; i < n; ++i) {
    if (g[i].size() > 2) {
      continue;
    }
    int h = max(dp[i], dp_up[i]);
    if (ans_h > h) {
      ans_h = h;
      ans_v = i;
    }
  }
  int ans = 1;
  for (int i = 0; i <= ans_h; ++i) {
    ans *= 2;
    ans %= M;
  }
  ans+= M - 1;
  ans %= M;
  ans += M - n;
  ans %= M;
  cout << ans_v + 1 << ' ' << ans << endl;
  return;
}

int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  int T;
  cin >> T;
  while (T-- > 0) {
    solve();
  }
}