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
sys.setrecursionlimit(10**5)

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

if M % 2 == 0 :
    vec = [[] for _ in range(N)]
    for _ in range(M) :
        A, B = map(int, input().split())
        vec[A-1].append(B-1)
        vec[B-1].append(A-1)

    visited = [False] * N
    CD = [[] for _ in range(N)]

    def dfs(cur, pre) :
        for nex in vec[cur] :
            if nex == pre :
                continue
            
            if not visited[nex] :
                visited[nex] = True
                dfs(nex, cur)
            elif not cur in CD[nex] :
                CD[cur].append(nex)
        
        if pre != -1 :
            if len(CD[cur]) % 2 == 0 :
                CD[pre].append(cur)
            else :
                CD[cur].append(pre)

    visited[0] = True            
    dfs(0, -1)

    for i in range(N) :
        for j in CD[i] :
            print(i + 1, j + 1)
else :
    print(-1)