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
read = sys.stdin.buffer.read
readline = sys.stdin.buffer.readline
readlines = sys.stdin.buffer.readlines
from heapq import heappop,heappush
from collections import defaultdict

n,m = map(int,readline().split())
ab = list(map(int,read().split()))

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

it = iter(ab)
links = [[] for _ in range(n+1)]
for a,b in zip(it,it):
    links[a].append(b)
    links[b].append(a)

depth = [-1] * (n+1)
parent = [0] * (n+1)
child = [set() for _ in range(n+1)]
hq_dep = []

stack = [1]
depth[1] = 0
# heappush(hq_dep, (0,1))
now_dep = 1
while(stack):
    stack2 = []
    while(stack):
        i = stack.pop()
        for j in links[i]:
            if(depth[j] == -1):
                depth[j] = now_dep
                parent[j] = i
                heappush(hq_dep,(now_dep*-1,j))
                stack2.append(j)
            else:
                child[j].add(i)
    now_dep += 1
    stack = stack2[::]

# 0:未定　1:done
ans = []
d = defaultdict(int)
outs = [0] * (n+1)
while(hq_dep):
    i_dep,i = heappop(hq_dep)
    for j in child[i]:
        if(d[min(i,j)*10**6 + max(i,j)] == 0):
            d[min(i,j)*10**6 + max(i,j)] = 1
            outs[j] += 1
            ans.append([j,i])
    j = parent[i]
    if(outs[i]%2==1):
        d[min(i,j)*10**6 + max(i,j)] = 1
        outs[i] += 1
        ans.append([i,j])
    else:
        d[min(i,j)*10**6 + max(i,j)] = 1
        outs[j] += 1
        ans.append([j,i])

print('\n'.join(map(lambda x: ' '.join(map(str,x)), ans)))