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
stdin = sys.stdin

sys.setrecursionlimit(10 ** 7)

def li(): return map(int, stdin.readline().split())
def li_(): return map(lambda x: int(x) - 1, stdin.readline().split())
def lf(): return map(float, stdin.readline().split())
def ls(): return stdin.readline().split()
def ns(): return stdin.readline().rstrip()
def lc(): return list(ns())
def ni(): return int(stdin.readline())
def nf(): return float(stdin.readline())



n, m = li()
edge = dict()
graph = [[] for _ in range(n)]
visited = [False]*n
par = [-1]*n
outs = [0]*n

for _ in range(m):
    a, b = li_()
    edge[(a, b)] = 0
    edge[(b, a)] = 0
    graph[a].append(b)
    graph[b].append(a)

def dfs(graph, visited, par, root, cur):

    for nex in graph[cur]:
        if visited[nex]:
            continue

        else:
            visited[nex] = True
            par[nex] = cur

            dfs(graph, visited, par, root, nex)

    if cur == root:
        return

    for neighbor in graph[cur]:
        if neighbor == par[cur]:
            continue

        if edge[(cur, neighbor)] != 0:
            continue

        edge[(cur, neighbor)] = 1
        edge[(neighbor, cur)] = -1

        outs[cur] += 1

    if outs[cur] % 2:
        edge[(cur, par[cur])] = 1
        edge[(par[cur], cur)] = -1
        outs[cur] += 1

    else:
        edge[(cur, par[cur])] = -1
        edge[(par[cur], cur)] = 1
        outs[par[cur]] += 1


if m % 2:
    print(-1)

else:
    visited[0] = True
    dfs(graph, visited, par, 0, 0)

    for (src, dst), val in edge.items():
        if val == 1:
            print(src+1, dst+1)