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:
import sys
from collections import deque

sys.setrecursionlimit(10 ** 5)


def solve(n, m, links):
    if m % 2 == 1:
        print(-1)
        return

    tree = [set() for _ in range(n)]
    parents = [-1] * n
    q = deque([0])
    while q:
        v = q.popleft()
        for u in links[v]:
            if parents[u] == -1:
                tree[v].add(u)
                parents[u] = v
                q.append(u)
            links[u].remove(v)

    parities = [len(l) % 2 for l in links]

    # print(links)
    # print(tree)
    # print(parents)
    # print(parities)

    def dfs(v):
        b = parities[v]
        for u in tree[v]:
            c = dfs(u)
            b ^= c
        if b:
            p = parents[v]
            links[p].remove(v)
            links[v].add(p)
        return b

    dfs(0)

    ans = ['{} {}'.format(v + 1, u + 1) for v in range(n) for u in links[v]]
    print('\n'.join(ans))


n, m = list(map(int, input().split()))

links = [set() for _ in range(n)]
for line in sys.stdin:
    a, b = map(int, line.split())
    a -= 1
    b -= 1
    links[a].add(b)
    links[b].add(a)

solve(n, m, links)