判了走完整个环的情况，代码下方那三个小范围的 hack 都过了，88pts 求调

#include <bits/stdc++.h>
using namespace std;
namespace lgh {
#define int long long
#define pii pair<int, int>
	
const int N = 5e5 + 5;
const int INF = 0x3f3f3f3f;

int n, m;

struct Edge {
	int to, pre;
};
Edge e[N * 2];
int idx = 1, head[N];
void addedge(int u, int v) {
	e[++idx] = {v, head[u]};
	head[u] = idx;
}

bool edgecut[N * 2];
int dfn[N], low[N], index;
bool instk[N];
void tarjan(int u, int lst) {
	dfn[u] = low[u] = ++index;
	instk[u] = 1;
	for(int i = head[u]; i; i = e[i].pre) {
		int v = e[i].to;
		if(v == lst) continue;
		if(!dfn[v]) {
			tarjan(v, u);
			low[u] = min(low[u], low[v]);
			if(low[v] > dfn[u]) {
				edgecut[i] = edgecut[i ^ 1] = 1;
			}
		} else if(instk[v]) {
			low[u] = min(low[u], dfn[v]);
		}
	}
	instk[u] = 0;
}
	
vector<int> ans;
bool vis[N];
int rec;
pii get(int u) {
	pii res;
	for(int i = head[u]; i; i = e[i].pre) {
		if(edgecut[i]) continue;
		int v = e[i].to;
		if(vis[v]) continue;
		if(!res.first) res.first = v;
		else res.second = v;
	}
	if(res.second && res.first > res.second) swap(res.first, res.second);
	return res;
}
void dfs(int u) {
	ans.push_back(u);
	pii t = get(u);
	
	if(!t.first) { // 当前点不在环上
		vector<int> son;
		for(int i = head[u]; i; i = e[i].pre) {
			int v = e[i].to;
			if(vis[v]) continue;
			son.push_back(v);
		}
		sort(son.begin(), son.end());
		for(auto &v : son) {
			vis[v] = 1;
			dfs(v);
		}
		return;
	}
	
	if(t.second) { // 当前点是关键点
		vector<int> son;
		int tar = t.first;
		rec = t.second;
		
//		printf("keyp %lld %lld %lld\n", u, tar, rec);
		
		for(int i = head[u]; i; i = e[i].pre) {
			int v = e[i].to;
			if(vis[v]) continue;
			if(v >= tar) continue;
			son.push_back(v);
		}
		sort(son.begin(), son.end());
		for(auto &v : son) {
			vis[v] = 1;
			dfs(v);
		}
		
		vis[tar] = 1;
		dfs(tar);
		
		son.clear();
		for(int i = head[u]; i; i = e[i].pre) {
			int v = e[i].to;
			if(vis[v]) continue;
			if(v >= rec) continue;
			son.push_back(v);
		}
		sort(son.begin(), son.end());
		for(auto &v : son) {
			vis[v] = 1;
			dfs(v);
		}
		
//		puts("------------------------");
		
		if(!vis[rec]) {
			vis[rec] = 1;
			int tmp = rec;
			rec = INF;
			dfs(tmp);
		}
		
		son.clear();
		for(int i = head[u]; i; i = e[i].pre) {
			int v = e[i].to;
			if(vis[v]) continue;
			son.push_back(v);
		}
		sort(son.begin(), son.end());
		for(auto &v : son) {
			vis[v] = 1;
			dfs(v);
		}
		return;
	}
	
	vector<int> son;
	int tar = t.first;
	
	for(int i = head[u]; i; i = e[i].pre) {
		int v = e[i].to;
		if(vis[v]) continue;
		if(v >= tar) continue;
		son.push_back(v);
	}
	sort(son.begin(), son.end());
	for(auto &v : son) {
		vis[v] = 1;
		dfs(v);
	}
	
	if(tar <= rec) {
		vis[tar] = 1;
		dfs(tar);
	} 
//	else printf("stop %lld %lld\n", u, tar);
	
	son.clear();
	for(int i = head[u]; i; i = e[i].pre) {
		int v = e[i].to;
		if(vis[v]) continue;
		if(v == tar) continue;
		son.push_back(v);
	}
	sort(son.begin(), son.end());
	for(auto &v : son) {
		vis[v] = 1;
		dfs(v);
	}
}

signed main() {
	scanf("%lld %lld", &n, &m);
	for(int i = 1; i <= m; ++i) {
		int u, v;
		scanf("%lld %lld", &u, &v);
		addedge(u, v);
		addedge(v, u);
	}
	
	tarjan(1, 0);
	
	vis[1] = 1;
	dfs(1);
	
	for(auto &i : ans) printf("%lld ", i);
	return 0;
}
}
signed main() {
// 	freopen("travel.in", "r", stdin);
// 	freopen("travel.out", "w", stdout);
	return lgh::main();
}

/*
hack1:
6 6
1 2
1 3
1 4
1 5
1 6
2 3
ans1:
1 2 3 4 5 6

hack2:
9 9
1 6
1 2
2 9
2 3
2 7
3 4
3 8
4 5
5 7
ans2:
1 2 3 4 5 7 8 9 6

hack3:
5 5
1 2
2 3
3 4
4 2
3 5
ans3:
1 2 3 4 5
*/