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
input = sys.stdin.readline

N, M = map(int, input().split())

X = [[] for i in range(N)]
k = 0
for i in range(M):
    x, y = map(int, input().split())
    X[x-1].append(y-1)
    X[y-1].append(x-1)
    k += 1

if k % 2:
    print(-1)
else:
    ANS = []
    P = [-1] * N
    Q = [(-1, 0)]
    done = [0] * N
    C = [0] * N
    R = []
    while Q:
        pre, i = Q.pop()
        if done[i]:
            C[i] += 1
            if pre >= 0:
                ANS.append((i, pre))
            continue
        done[i] = 1
        R.append(i)
        for a in X[i]:
            if a != P[i]:
                P[a] = i
                X[a].remove(i)
                Q.append((i, a))

    for i in R[1:][::-1]:
        if C[i] % 2:
            ANS.append((i, P[i]))
        else:
            ANS.append((P[i], i))
            C[P[i]] += 1
    for a, b in ANS:
        print(a+1, b+1)