eolymp
Competitions

Bipartite graphs

Chef and Bipartite Graph

Chef is very interested in studying biparite graphs. Today he wants to construct a bipartite graph with n vertices each, on the two parts, and with total number of edges equal to m. The vertices on the left are numbered from 1 to n. And the vertices on the right are also numbered from 1 to n. He also wants the degree of every vertex to be greater than or equal to d, and to be lesser than or equal to D. ie. for all v: ddeg(v)D.

Given four integers n, m, d, D you have to help Chef in constructing some bipartite graph satisfying this property. If there does not exist any such graph, output -1.

Input

First line contains the number of test cases t.

The only line of each test case contains four integers n (1n100), m (0mn * n), d, D (1dDn).

Output

For each test case, output -1 if there is no bipartite graph satisfying this property. Otherwise output m lines, each of the lines should contain two integers u, v denoting that there is an edge between vertex u on the left part and vertex v on the right part. If there can be multiple possible answers, you can print any. Note that the bipartite graph should not have multi-edges.

Time limit 1 second
Memory limit 128 MiB
Input example #1
2
2 3 1 2
2 3 1 1
Output example #1
1 1
2 2
1 2
-1