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
sys.setrecursionlimit(10**7)
input = sys.stdin.readline

n, m = map(int, input().split())
g = [[] for _ in range(n)]
for i in range(m):
    a, b = map(int, input().split())
    a -= 1
    b -= 1
    g[a].append(b)
    g[b].append(a)

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

ans = []

depth = [-1] * n
deg = [0] * n
def dfs(v, pr):
    for nv in g[v]:
        if nv == pr:
            continue
        if depth[nv] != -1:
            # 全域木以外のところを処理する
            # 重複して辺を繋げるのを防ぐ
            if depth[nv] < depth[v]:
                ans.append((v, nv))
                deg[v] += 1
        else:
            depth[nv] = depth[v] + 1
            dfs(nv, v)
            if deg[nv] % 2 == 0:
                ans.append((v, nv))
                deg[v] += 1
            else:
                ans.append((nv, v))
                deg[nv] += 1

depth[0] = 0
dfs(0, -1)

for i, j in ans:
    print(i + 1, j + 1)