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
sys.setrecursionlimit(1000000)

nVertices, nEdges = map(int, input().split())
edges = [[] for _ in range(nVertices + 1)]
for _ in range(nEdges):
    u, v = map(int, input().split())
    edges[u].append(v)
    edges[v].append(u)

if nEdges & 1 == 1:
    print(-1)
    exit()

def dfs(v):
    visited[v] = True
    for next in edges[v]:
        if not visited[next]:
            mst[v].add(next)
            mst[next].add(v)
            dfs(next)

def dfs2(par, v):
    for child in mst[v]:
        if child != par:
            dfs2(v, child)
    if par == 0:
        return
    if len(out[v]) & 1 == 1:
        out[v].add(par)
    else:
        out[par].add(v)

mst = [set() for _ in range(nVertices + 1)]
visited = [False] * (nVertices + 1)
dfs(1)

out = [set() for _ in range(nVertices + 1)]
for u in range(1, nVertices + 1):
    for v in edges[u]:
        if v not in mst[u] and u not in out[v]:
            out[u].add(v)

dfs2(0, 1)
for u in range(1, nVertices + 1):
    for v in out[u]:
        print(u, v)