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


class UnionFind:
    """素集合を木構造として管理する"""
    def __init__(self, n):
        self.parent = [-1] * n
        self.cnt = n

    def root(self, x):
        """要素xの根を求める"""
        if self.parent[x] < 0:
            return x
        else:
            self.parent[x] = self.root(self.parent[x])
            return self.parent[x]

    def merge(self, x, y):
        """要素xを含む集合と要素yを含む集合を統合する"""
        x = self.root(x)
        y = self.root(y)
        if x == y:
            return
        if self.parent[x] > self.parent[y]:
            x, y = y, x
        self.parent[x] += self.parent[y]
        self.parent[y] = x
        self.cnt -= 1

    def is_same(self, x, y):
        """要素x, yが同じ集合に属するかどうかを求める"""
        return self.root(x) == self.root(y)

    def get_size(self, x):
        """要素xを含む集合の要素数を求める"""
        return -self.parent[self.root(x)]


n, m = map(int, input().split())
info = [list(map(int, input().split())) for i in range(m)]

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

uf = UnionFind(n)
tree = [[] for i in range(n)]
out_deg = [0] * n
ans = []
for u, v in info:
    u, v = u - 1, v - 1
    if uf.is_same(u, v):
        ans.append((u + 1, v + 1))
        out_deg[u] += 1
    else:
        uf.merge(u, v)
        tree[u].append(v)
        tree[v].append(u)
        
root = 0
q = deque([root])
par = {0: -1}
topo = []
while q:
    v = q.popleft()
    topo.append(v)
    for nxt_v in tree[v]:
        if nxt_v in par:
            continue
        par[nxt_v] = v
        q.append(nxt_v)
        
while topo:
    v = topo.pop()
    if v == 0:
        break
    if out_deg[v] % 2 == 1:
        out_deg[v] += 1
        ans.append((v + 1, par[v] + 1))
    else:
        out_deg[par[v]] += 1
        ans.append((par[v] + 1, v + 1))

for res in ans:
    print(*res)