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.*;
import java.util.*;
import java.util.function.Function;

public class Main {

    static int N, M;
    static List<Edge> E;

    public static void main(String[] args) {
        FastScanner sc = new FastScanner(System.in);
        N = sc.nextInt();
        M = sc.nextInt();
        E = new ArrayList<>(M);
        for (int i = 0; i < M; i++) {
            E.add(new Edge(sc.nextInt()-1, sc.nextInt()-1));
        }

        PrintWriter pw = new PrintWriter(System.out);
        solve(pw);
        pw.flush();
    }

    static void solve(PrintWriter pw) {
        if( M % 2 == 1 ) {
            pw.println(-1);
            return;
        }

        Edge[][] G = adjB(N, E);
        Edge[][] T = mkTree();
        for (Node node : orderFromLeaf(N, T, 0)) {
            // 残ってるのが偶数なら全部消費する
            // そうでないなら親へのEdge以外を消費する
            int cnt = 0;
            for (Edge e : G[node.a]) {
                if( !e.used ) {
                    cnt++;
                }
            }

            for (Edge e : G[node.a]) {
                if( e.used ) continue;

                int b = e.opposite(node.a);
                if( b == node.parent && cnt % 2 == 1 ) continue; // 親に任せる

                pw.println((node.a+1) + " " + (b+1));
                e.used = true;
            }
        }
    }

    static class Node {
        int parent, a;

        public Node(int parent, int a) {
            this.parent = parent;
            this.a = a;
        }
    }

    static Node[] orderFromLeaf(int N, Edge[][] G, int root) {
        ArrayDeque<Node> q = new ArrayDeque<>();
        Node[] ret = new Node[N];
        int idx = N-1;
        q.add(new Node(-1, root));
        while(!q.isEmpty()) {
            Node n = q.poll();
            ret[idx--] = n;
            for (Edge e : G[n.a]) {
                int next = e.opposite(n.a);
                if( next == n.parent ) continue;

                q.add(new Node(n.a, next));
            }
        }
        return ret;
    }

    static Edge[][] mkTree() {
        UnionFind uf = new UnionFind(N);
        List<Edge> es = new ArrayList<>();
        for (int i = 0; i < M; i++) {
            Edge e = E.get(i);
            if( !uf.isSame(e.a, e.b) ) {
                uf.unite(e.a, e.b);
                es.add( e );
            }
        }

        return adjB(N, es);
    }

    static class UnionFind {

        private final int[] parent;
        private final int[] count;

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

        public int root(int i) {
            if (parent[i] == i) {
                return i;
            } else {
                return parent[i] = root(parent[i]);
            }
        }

        public int unite(int i, int j) {
            int ri = root(i);
            int rj = root(j);
            if (ri == rj) return ri;


            int big = count[ri] < count[rj] ? rj : ri;
            int small = big == ri ? rj : ri;
            parent[small] = big;
            count[big] += count[small];
            return big;
        }

        public int count(int a) {
            return count[root(a)];
        }

        public boolean isSame(int a, int b) {
            return root(a) == root(b);
        }
    }

    static class Edge {
        int a, b;
        boolean used;

        public Edge(int a, int b) {
            this.a = a;
            this.b = b;
        }

        public int opposite(int x) {
            return a == x ? b : a;
        }
    }

    static Edge[][] adjB(int n, List<Edge> E) {
        Edge[][] adj = new Edge[n][];
        int[] cnt = new int[n];
        for (Edge e : E) {
            cnt[e.a]++;
            cnt[e.b]++;
        }
        for (int i = 0; i < n; i++) {
            adj[i] = new Edge[cnt[i]];
        }
        for (Edge e : E) {
            adj[e.a][--cnt[e.a]] = e;
            adj[e.b][--cnt[e.b]] = e;
        }
        return adj;
    }

    static int[][] adjB(int n, int[] from, int[] to) {
        int[][] adj = new int[n][];
        int[] cnt = new int[n];
        for (int f : from) {
            cnt[f]++;
        }
        for (int t : to) {
            cnt[t]++;
        }
        for (int i = 0; i < n; i++) {
            adj[i] = new int[cnt[i]];
        }
        for (int i = 0; i < from.length; i++) {
            adj[from[i]][--cnt[from[i]]] = to[i];
            adj[to[i]][--cnt[to[i]]] = from[i];
        }
        return adj;
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

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

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken("\n");
        }

        long nextLong() {
            return Long.parseLong(next());
        }

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

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        int[] nextIntArray(int n, int delta) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt() + delta;
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++)
                a[i] = nextLong();
            return a;
        }
    }

    static <A> void writeLines(A[] as, Function<A, String> f) {
        PrintWriter pw = new PrintWriter(System.out);
        for (A a : as) {
            pw.println(f.apply(a));
        }
        pw.flush();
    }

    static void writeLines(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int a : as) pw.println(a);
        pw.flush();
    }

    static void writeLines(long[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (long a : as) pw.println(a);
        pw.flush();
    }

    static int max(int... as) {
        int max = Integer.MIN_VALUE;
        for (int a : as) max = Math.max(a, max);
        return max;
    }

    static int min(int... as) {
        int min = Integer.MAX_VALUE;
        for (int a : as) min = Math.min(a, min);
        return min;
    }

    static void debug(Object... args) {
        StringJoiner j = new StringJoiner(" ");
        for (Object arg : args) {
            if (arg instanceof int[]) j.add(Arrays.toString((int[]) arg));
            else if (arg instanceof long[]) j.add(Arrays.toString((long[]) arg));
            else if (arg instanceof double[]) j.add(Arrays.toString((double[]) arg));
            else if (arg instanceof Object[]) j.add(Arrays.toString((Object[]) arg));
            else j.add(arg.toString());
        }
        System.err.println(j.toString());
    }
}