Codeforces Round 335 (Div. 1) |
---|

Finished |

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

constructive algorithms

data structures

graphs

*1700

No tag edit access

The problem statement has recently been changed. View the changes.

×
B. Lazy Student

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputStudent Vladislav came to his programming exam completely unprepared as usual. He got a question about some strange algorithm on a graph — something that will definitely never be useful in real life. He asked a girl sitting next to him to lend him some cheat papers for this questions and found there the following definition:

The minimum spanning tree *T* of graph *G* is such a tree that it contains all the vertices of the original graph *G*, and the sum of the weights of its edges is the minimum possible among all such trees.

Vladislav drew a graph with *n* vertices and *m* edges containing no loops and multiple edges. He found one of its minimum spanning trees and then wrote for each edge its weight and whether it is included in the found tree or not. Unfortunately, the piece of paper where the graph was painted is gone and the teacher is getting very angry and demands to see the original graph. Help Vladislav come up with a graph so that the information about the minimum spanning tree remains correct.

Input

The first line of the input contains two integers *n* and *m* () — the number of vertices and the number of edges in the graph.

Each of the next *m* lines describes an edge of the graph and consists of two integers *a*_{j} and *b*_{j} (1 ≤ *a*_{j} ≤ 10^{9}, *b*_{j} = {0, 1}). The first of these numbers is the weight of the edge and the second number is equal to 1 if this edge was included in the minimum spanning tree found by Vladislav, or 0 if it was not.

It is guaranteed that exactly *n* - 1 number {*b*_{j}} are equal to one and exactly *m* - *n* + 1 of them are equal to zero.

Output

If Vladislav has made a mistake and such graph doesn't exist, print - 1.

Otherwise print *m* lines. On the *j*-th line print a pair of vertices (*u*_{j}, *v*_{j}) (1 ≤ *u*_{j}, *v*_{j} ≤ *n*, *u*_{j} ≠ *v*_{j}), that should be connected by the *j*-th edge. The edges are numbered in the same order as in the input. The graph, determined by these edges, must be connected, contain no loops or multiple edges and its edges with *b*_{j} = 1 must define the minimum spanning tree. In case there are multiple possible solutions, print any of them.

Examples

Input

4 5

2 1

3 1

4 0

1 1

5 0

Output

2 4

1 4

3 4

3 1

3 2

Input

3 3

1 0

2 1

3 1

Output

-1

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jun/08/2023 15:27:26 (k2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|