A Romanian software company has bought N computers, which are going to be connected so that they may form a network. A connection can be made between any 2
distinct computers and is bidirectional (if the 2 computers are labeled i and j, then data can be sent both from i to j and from j to i). Your job is to determine a way to connect all the N computers, in such a way that every 2 computers will be able to send data between them (directly or using other computers as intermediate devices).
There is only one extra requirement: the network must contain exactly K critical pairs. A pair (i, j) is critical if there exists a connection which, if removed, data communication between i and j will become impossible.
The input consists of 2 integer numbers: N (1 ≤ N ≤ 100), the number of computers
the network will contain and K (0 ≤ K ≤ N*(N-1)/2), the number of critical pairs the network will contain.
You should output the connections which form the network, one connection per line. A connection is described by a pair (i, j), which means that i and j are directly connected. The 2 numbers of the pair should be separated by a blank. If you cannot
build a network which contains exactly K critical pairs, then you should output -1.
Problem Author: Mugurel Ionut Andreica
Problem Source: Romanian Open Contest, December 2001