Problem:
Score : 700 points

Problem Statement

You are given a simple connected undirected graph with N vertices and M edges. The vertices are numbered 1 to N, and the i-th edge connects Vertex A_i and Vertex B_i.
Takahashi will assign one of the two possible directions to each of the edges in the graph to make a directed graph.
Determine if it is possible to make a directed graph with an even number of edges going out from every vertex. If the answer is yes, construct one such graph.

Notes

An undirected graph is said to be simple when it contains no self-loops or multiple edges.

Constraints

2 \leq N \leq 10^5

N-1 \leq M \leq 10^5

1 \leq A_i,B_i \leq N (1\leq i\leq M)

The given graph is simple and connected.

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
:
A_M B_M

Output

If it is impossible to assign directions to satisfy the requirement, print -1.
Otherwise, print an assignment of directions that satisfies the requirement, in the following format:

C_1 D_1
:
C_M D_M

Here each pair (C_i, D_i) means that there is an edge directed from Vertex C_i to Vertex D_i. The edges may be printed in any order.

Sample Input 1

4 4
1 2
2 3
3 4
4 1

Sample Output 1

1 2
1 4
3 2
3 4

After this assignment of directions, Vertex 1 and 3 will each have two outgoing edges, and Vertex 2 and 4 will each have zero outgoing edges.

Sample Input 2

5 5
1 2
2 3
3 4
2 5
4 5

Sample Output 2

-1

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define rep(i,N) for(int i=0,i##_max=(N);i<i##_max;++i)
#define repp(i,l,r) for(int i=(l),i##_max=(r);i<i##_max;++i)
#define per(i,N) for(int i=(N)-1;i>=0;--i)
#define perr(i,l,r) for(int i=r-1,i##_min(l);i>=i##_min;--i)
#define all(arr) (arr).begin(), (arr).end()
#define SP << " " <<
#define SPF << " "
#define SPEEDUP cin.tie(0);ios::sync_with_stdio(false);
#define MAX_I INT_MAX //1e9
#define MIN_I INT_MIN //-1e9
#define MAX_UI UINT_MAX //1e9
#define MAX_LL LLONG_MAX //1e18
#define MIN_LL LLONG_MIN //-1e18
#define MAX_ULL ULLONG_MAX //1e19
  typedef long long ll;
  typedef pair<int,int> PII;
  typedef pair<char,char> PCC;
  typedef pair<ll,ll> PLL;
  typedef pair<char,int> PCI;
  typedef pair<int,char> PIC;
  typedef pair<ll,int> PLI;
  typedef pair<int,ll> PIL; 
  typedef pair<ll,char> PLC; 
  typedef pair<char,ll> PCL; 

inline void YesNo(bool b){ cout << (b?"Yes" : "No") << endl;}
inline void YESNO(bool b){ cout << (b?"YES" : "NO") << endl;}
inline void Yay(bool b){ cout << (b?"Yay!" : ":(") << endl;}

const int N_MAX = 1e5 + 10;
const int M_MAX = 1e5 + 10;
vector<int> G[N_MAX];
vector<int> H[N_MAX];
vector<int> tree[N_MAX];
vector<int> d(N_MAX,0);
int N,M;

class UnionFind{
  private:
    vector<int> Parent;
  public:
    UnionFind(int N){
      Parent = vector<int>(N,-1);
    }

    int find(int x){
      if(Parent[x]<0)return x;
      return Parent[x] = find(Parent[x]);
    }

    int size(int x){
      return -Parent[find(x)];
    }

    bool unite(int x, int y){
      x = find(x);
      y = find(y);
      if(x==y)return false;

      if(x<y)swap(x,y);
      Parent[x] += Parent[y];
      Parent[y] = x;
      return true;
    }

    bool same(int x, int y){
      return find(x) == find(y);
    }
};


void dfs(int cur,int pare){
  for(int &e : tree[cur]){
    if(e == pare)continue;
    dfs(e,cur);
  }
  if(pare!=-1){
    if(d[cur]&1){
      cout << cur SP pare << endl;
      ++d[cur];
    }else{
      cout << pare SP cur << endl;
      ++d[pare];
    }
  }
}

int main(void){
  SPEEDUP
  cout << setprecision(15);
  cin >> N >> M;
  rep(i,M){
    int x,y;cin >> x >> y;
    G[x].push_back(y);
    G[y].push_back(x);
  }
  if(M&1){
    cout << -1 << endl;
    return 0;
  }
  //全域木を作る
  set<PII> st;
  queue<int> que;
  que.push(1);
  UnionFind uni = UnionFind(N+1);
  while(!que.empty() && uni.size(1) != N){
    int x = que.front();que.pop();
    for(int &e : G[x]){
      if(uni.same(e,x))continue;
      uni.unite(e,x);
      que.push(e);
      tree[x].push_back(e);
      tree[e].push_back(x);
      st.insert(PII(x,e));
      st.insert(PII(e,x));
    }
  }

  //木以外の辺を適当につける
  rep(x,N){
    for(int &e :G[x]){
      if(st.count(PII(e,x)))continue;
      cout << e SP x << endl;
      ++d[e];
    }
  }

  //木の辺をつける
  dfs(1,-1);
  return 0;
}