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
# Your code here!
from collections import deque
import sys
sys.setrecursionlimit(10**6)
readline = sys.stdin.readline #文字列入力のときは注意

n,m = [int(i) for i in readline().split()]

if m%2: print(-1); exit()

#L = [0]*n

g = [[] for _ in range(n)]
for i in range(m):
    a,b = [int(i) for i in readline().split()]
    g[a-1].append((b-1,i))
    g[b-1].append((a-1,i))
#    L[a-1] += 1
#    L[b-1] += 1



used = [0]*m
usedp = [0]*n
def dfs(v):
    res = 0
    for (c,i) in g[v]:
        if used[i] == 1: continue
        used[i] = 1
        if usedp[c] == 1:
            res += 1
            print(v+1,c+1)
            continue
        usedp[c] = 1
        p =  dfs(c)
        if p%2 == 1:
            print(v+1,c+1)
        else:    
            print(c+1,v+1)
        res += p
    return res+1


for i in range(n):
    dfs(i)
#print(q)