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 $v:d\le deg(v)\le D$.

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 $n(1\le n\le 100)$, $m(0\le m\le n\cdot n)$, $d,D(1\le d\le D\le n)$.

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.

Examples