#include<bits/stdc++.h>
#define pb push_back
#define fast ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0)
#define ll long long
#define pii pair<int,int>
#define pll pair<ll,ll>
#define f first
#define s second
#define int long long
#define sz(x) (ll)(x.size())
using namespace std;
const int mod = 1e9+7;
int expo_pow(int x,int y){
if(y == 0) return 1;
y=y%(mod-1);
x%=mod;
if(y==0) y=mod-1;
int res=1;
while(y){
if(y&1) res=(res*x)%mod;
x=(x*x)%mod;
y>>=1;
}
return res;
}
ll add()
{
return 0;
}
template <typename T, typename... Types>
T add(T var1, Types... var2){
return (((((ll)(var1)) % mod + (ll)(add(var2...))) % mod) + mod) % mod;
}
ll mul(){
return 1;
}
template <typename T, typename... Types>
T mul(T var1, Types... var2){
return (((ll)(var1)) % mod * (ll)(mul(var2...))) % mod;
}
int n,m;
vector<vector<int>> adj;
int cnt_cric,bridges;
vector<vector<int>> adj2;
vector<bool> visited;
vector<int> tin,low;
vector<bool> is_cut;
int timer,comp,mx_comp;
int cur_comp;
int cut_count = 0;
vector<vector<bool>> done;
void init() {
adj.clear();
adj.resize(n+1);
adj2.clear();
adj2.resize(n+1);
tin.clear();
tin.resize(n+1);
low.clear();
low.resize(n+1);
visited.clear();
visited.assign(n+1,0);
is_cut.clear();
is_cut.assign(n+1,0);
done.clear();
done.assign(n+1,vector<bool>(n+1,0));
cnt_cric = 0;
bridges = 0;
timer = 0;
comp = 0;
mx_comp = 0;
}
void dfs(int v,int p = -1) {
visited[v] = 1;
tin[v] = low[v] =timer++;
int children = 0;
for (auto u:adj[v]) {
if (u == p) continue;
if (visited[u]) {
if (done[u][v] == 0) {
adj2[u].pb(v);
adj2[v].pb(u);
done[u][v] = 1;
done[v][u] = 1;
}
low[v] = min(tin[u],low[v]);
}
else {
dfs(u,v);
low[v] = min(low[u],low[v]);
if (low[u] >= tin[v] and p != -1) {
is_cut[v] = 1;
}
if (low[u] > tin[v]) {
bridges++;
} else {
if (done[u][v] == 0) {
adj2[u].pb(v);
adj2[v].pb(u);
done[u][v] = 1;
done[v][u] = 1;
}
}
++children;
}
}
if (p == -1 and children > 1) {
is_cut[v] = 1;
}
}
void dfs2(int cur,int par = -1) {
if (is_cut[cur] == 1 and cut_count == 0){
cut_count++;
return;
}
visited[cur] = 1;
for (auto u:adj2[cur]) {
if (u == par) continue;
if (visited[u] == 1) {
if (done[u][cur] == 0) {
cur_comp++;
done[u][cur] = 1;
done[cur][u] = 1;
}
}
else {
dfs2(u,cur);
if (done[u][cur] == 0) {
cur_comp++;
done[u][cur] = 1;
done[cur][u] = 1;
}
}
}
}
void solve(){
cin >> n >> m;
init();
for (int i = 0; i < m; ++i) {
int p,q;
cin >> p >> q;
adj[p].pb(q);
adj[q].pb(p);
}
dfs(1);
visited.clear();
visited.assign(n+1,0);
done.assign(n+1,vector<bool>(n+1,0));
for (int i = 1; i <= n; ++i) {
if (visited[i] == 0 and is_cut[i] == 0) {
cut_count = 0;
cur_comp = 0;
dfs2(i);
mx_comp = max(cur_comp,mx_comp);
if(cur_comp != 0) comp++;
}
}
for (int i = 1; i <= n; ++i) {
if (is_cut[i]) cnt_cric++;
}
int p = max(1LL,comp + bridges);
int q = max(1LL,mx_comp);
int g = __gcd(p,q);
p /= g;
q /= g;
cout << cnt_cric << " " << bridges << " " << p << " " << q << "\n";
}
signed main(){
fast;
int test = 1;
cin>>test;
int i=1;
while(test--){
solve();
}
}