Eulerian circuit - DFS with Stack

#include <bits/stdc++.h>

using namespace std;

ifstream fin("ciclueuler.in");
ofstream fout("ciclueuler.out");

int main() {
    int N, M;
    fin >> N >> M;
    vector < vector < pair < int , int > > > G(N + 1);
    vector < bool > viz(M);
    for(int i = 0; i < M; ++i) {
        int u, v;
        fin >> u >> v;
        G[u].emplace_back(v, i);
        G[v].emplace_back(u, i);
    }
    for(int i = 1; i <= N; ++i)
        if(G[i].size() & 1) {
            fout << -1;
            return 0;
        }
    vector < int > sol;
    stack < int > S;
    S.emplace(1);
    while(!S.empty()) {
        int node = S.top();
        if(!G[node].empty()) {
            auto next = G[node].back();
            G[node].pop_back();
            if(!viz[next.second]) {
                viz[next.second] = true;
                S.emplace(next.first);
            }
        }
        else {
            S.pop();
            sol.emplace_back(node);
        }
    }
    sol.pop_back();
    for(int node : sol)
        fout << node << ' ';
}