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 PYTHON3):

Solution:
# -*- coding: utf-8 -*-
def solve():
    N, M = map(int, input().split())
    if M%2:
        return '-1'
    E = [set() for _ in range(N+1)]
    for _ in range(M):
        a,b = map(int, input().split())
        E[a].add(b)
        E[b].add(a)
    q = [(0,1,1)]
    v = set()
    T = []
    while q:
        n_, n, d = q.pop()
        if n not in v:
            T.append((d,n_,n))
            E[n].discard(n_)
            E[n_].discard(n)
            v.add(n)
            if E[n]-v:
                q.extend([(n,u, d+1) for u in E[n]-v])

    A = [0 for _ in range(N+1)]
    res = []
    c = set()
    for d,a,b in sorted(T, reverse=1)[:-1]:
        F = E[b]-c
        if A[b]%2 == 0 or len(E[b])%2:
            res.extend([(u,b) for u in F])
            for u in F:
                A[u] += 1
                E[u] -= {b}
        else:
            res.extend([(b,u) for u in F])
            for u in F:
                A[b] += 1
                E[u] -= {b}

        E[a] -= {b}
        if A[b]%2:
            A[b] += 1
            res.extend([(b,a)]) 
        else:
            A[a] += 1
            res.extend([(a,b)])

    return '\n'.join(['{} {}'.format(*e) for e in res])


if __name__ == '__main__':
    print(solve())