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:
from collections import deque
import sys

input = sys.stdin.readline

sys.setrecursionlimit(10 ** 6)

n, m = map(int, input().split())

if m & 1:
    print(-1)
    exit()

g = [set() for _ in range(n + 1)]
for _ in range(m):
    a, b = map(int, input().split())
    g[a].add(b)
    g[b].add(a)

seen = [False] * (n + 1)
seen[1] = True

mst = [set() for _ in range(n + 1)]

dq = deque()
dq.append(1)

while dq:
    v = dq.popleft()

    for u in g[v]:
        if seen[u]:
            continue
        seen[u] = True

        mst[u].add(v)
        mst[v].add(u)

        dq.append(u)

ans = set()
deg = [0] * (n + 1)
for v in range(1, n + 1):
    for u in g[v]:
        if v > u: continue
        if u not in mst[v]:
            ans.add((u, v))
            deg[u] += 1


def dfs(v, pr):
    for u in mst[v]:
        if u == pr:
            continue
        dfs(u, v)

    if pr == -1:
        return

    if deg[v] % 2 == 0:
        ans.add((pr, v))
        deg[pr] += 1
    else:
        ans.add((v, pr))
        deg[v] += 1


dfs(1, -1)

for aa in ans:
    print(*aa)