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:
if __name__ == '__main__':
    n, m = map(int, input().split())
    es = [None] * n
    for i in range(n):
        es[i] = []

    for a, b in (map(lambda x: int(x) - 1, input().split()) for _ in range(m)):
        es[a].append(b)
        es[b].append(a)

    if m % 2:
        print(-1)
        quit(0)

    mst_es = [None] * n
    for i in range(n):
        mst_es[i] = set()
    st = []
    used = [False] * n
    st.append(0)
    used[0] = True
    degrees = [0] * n
    num_edges = [0] * n
    while st != []:
        v = st.pop()
        for u in es[v]:
            if used[u]:
                if v not in mst_es[u] and u < v:
                    print(u + 1, v + 1)
                    degrees[u] += 1
            else:
                num_edges[u] += 1
                num_edges[v] += 1
                used[u] = True
                a, b = (u, v) if u < v else (v, u)
                st.append(u)
                mst_es[a].add(b)
                mst_es[b].add(a)

    st = [v for v in range(n) if num_edges[v] == 1]
    while st != []:
        v = st.pop()
        if num_edges[v] < 1:
            continue
        for u in mst_es[v]:
            a, b = (v, u) if degrees[v] % 2 == 1 else (u, v)
            print(a + 1, b + 1)
            degrees[a] += 1
        num_edges[u] -= 1
        num_edges[v] -= 1
        mst_es[v].remove(u)
        mst_es[u].remove(v)
        if num_edges[u] == 1:
            st.append(u)