Problem: 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.

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.

Examples

Input

4 4
1 2
2 3
3 4
4 1


Output

1 2
1 4
3 2
3 4


Input

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


Output

-1

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.PriorityQueue;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.HashSet;
import java.util.AbstractCollection;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Comparator;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author anand.oza
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        BEvenDegrees solver = new BEvenDegrees();
        solver.solve(1, in, out);
        out.close();
    }

    static class BEvenDegrees {
        int[] score;
        StringBuilder sb;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt(), m = in.nextInt();

            score = new int[n];

            PriorityQueue<Vertex> vertices = new PriorityQueue<>(Comparator.comparingInt(v -> v.degree));

            HashSet<Integer>[] adj = new HashSet[n];
            UnionFind uf = new UnionFind(n);
            for (int i = 0; i < n; i++)
                adj[i] = new HashSet<>();

            sb = new StringBuilder();

            for (int i = 0; i < m; i++) {
                int a = in.nextInt() - 1;
                int b = in.nextInt() - 1;
                boolean tree = uf.union(a, b);
                if (tree) {
                    adj[a].add(b);
                    adj[b].add(a);
                } else {
                    direct(a, b);
                }
            }

            for (int i = 0; i < n; i++) {
                vertices.add(new Vertex(i, adj[i].size()));
            }

            while (!vertices.isEmpty()) {
                Vertex v = vertices.poll();
                if (v.degree == 0)
                    continue;
                if (v.degree > adj[v.i].size())
                    continue;

                if (v.degree == 1) {
                    for (int j : adj[v.i]) {
                        adj[j].remove(v.i);
                        vertices.add(new Vertex(j, adj[j].size()));
                        if (score[v.i] == 1) {
                            score[v.i] ^= 1;
                            append(sb, v.i, j);
                        } else {
                            score[j] ^= 1;
                            append(sb, j, v.i);
                        }
                    }
                    adj[v.i].clear();
                    continue;
                }
            }

            boolean possible = true;
            for (int x : score) {
                if (x == 1)
                    possible = false;
            }

            out.println(possible ? sb.toString() : "-1");
        }

        void direct(int i, int j) {
            score[i] ^= 1;
            sb.append(String.format("%d %d%n", i + 1, j + 1));
        }

        static void append(StringBuilder sb, int i, int j) {
            sb.append(String.format("%d %d%n", i + 1, j + 1));
        }

        private class Vertex {
            final int i;
            final int degree;

            private Vertex(int i, int degree) {
                this.i = i;
                this.degree = degree;
            }

        }

    }

    static class UnionFind {
        private int[] __rep;
        private int[] __size;

        public UnionFind(int n) {
            __rep = new int[n];
            __size = new int[n];
            for (int i = 0; i < n; i++) {
                __rep[i] = i;
                __size[i] = 1;
            }
        }

        public int rep(int x) {
            if (__rep[x] == x) {
                return x;
            }

            int r = rep(__rep[x]);
            __rep[x] = r;
            return r;
        }

        public int size(int x) {
            return __size[rep(x)];
        }

        public boolean union(int x, int y) {
            x = rep(x);
            y = rep(y);

            if (x == y) {
                return false;
            }

            if (size(x) < size(y)) {
                int t = x;
                x = y;
                y = t;
            }

            // now size(x) >= size(y)

            __rep[y] = x;
            __size[x] += __size[y];
            return true;
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}