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 ** 6)
N, M = map(int, input().split())

if M % 2 != 0:
    print(-1)
    exit()

G = [[] for i in range(N)]
E = []
for i in range(M):
    a, b = map(int, input().split())
    a, b = a - 1, b - 1
    G[a].append(b)
    G[b].append(a)
    E.append((a, b))

visited = [False] * N
T = [set() for i in range(N)]
que = [0]
while que:
    u = que.pop()
    for w in G[u]:
        if visited[w]:
            continue
        visited[w] = True
        T[u].add(w)
        T[w].add(u)
        que.append(w)


ans = []
deg = [0] * N
for a, b in E:
    if b in T[a]:
        continue
    ans.append((a, b))
    deg[a] += 1


def dfs(u, p):
    for w in T[u]:
        if w == p:
            continue
        dfs(w, u)
        if deg[w] % 2 != 0:
            ans.append((w, u))
            deg[w] += 1
        else:
            ans.append((u, w))
            deg[u] += 1


dfs(0, -1)
for a, b in ans:
    print(a + 1, b + 1)