https://pintia.cn/problem-sets/1813039306479005696/exam/problems/type/7?problemSetProblemId=1813039385617129475&page=0

#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<ll, ll> PII;
typedef vector<long long> VI;
#define int long long
#define INF 0x3f3f3f3f
#define endl '\n'
#define N 200010
const int mod = 1e9 + 7;

ll lowbit(ll x) {
    return -x & x;
}

int p[N], si[N];
int find(int x) {
    if (x == p[x])return p[x];
    p[x] = find(p[x]);
    return p[x];
}
//size[find(b)] += size[find(a)];
//p[find(a)] = find(b)

int n, m, cnt, ans, d[N];
vector<int> g[N];

void dfs(int x) { //遍历搜环的大小
    d[x] = 0;

    for (auto t : g[x]) {
        if (d[t]) {
            cnt ++;
            dfs(t);
        }
    }
}
void bfs() { // 无向图去枝，只保留环

    queue<int> q;
    for (int i = 1; i <= n; i++) {
        if (d[i] == 1)q.push(i);
    }

    while (q.size()) {
        auto t = q.front();
        q.pop();
        d[t] --;

        for (auto now : g[t]) {
            d[now] --;

            if (d[now] == 1) {
                q.push(now);
            }
        }
    }
}
void solve() {
    cin >> n >> m;

    for (int i = 1; i <= n; i++) {
        g[i].clear();
        d[i] = 0;
    }

    for (int i = 1; i <= m; i++) {
        int u, v;
        cin >> u >> v;
        g[u].push_back(v);
        g[v].push_back(u);

        d[u] ++;
        d[v] ++;
    }

    bfs();

    //如图有个环，直接跑一遍dfs清度数
    for (int i = 1; i <= n; i++) {
        if (d[i] > 2)dfs(i);
    }

    ans = cnt = 0;

    for (int i = 1; i <= n; i++) {
        if (d[i] == 2) {
            ans ++;
            cnt = 1;
            dfs(i);
        }
    }

    if(ans == 1)cout << "Yes " << cnt << endl;
    else cout << "No " << ans << endl; 
}

signed main() {

    ios::sync_with_stdio(false);
    cin.tie(0), cout.tie(0);

    int T = 1;
    cin >> T;
    while (T --)

        solve();

    return 0;
}