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C. Searching for Graph

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLet's call an undirected graph of *n* vertices *p*-interesting, if the following conditions fulfill:

- the graph contains exactly 2
*n*+*p*edges; - the graph doesn't contain self-loops and multiple edges;
- for any integer
*k*(1 ≤*k*≤*n*), any subgraph consisting of*k*vertices contains at most 2*k*+*p*edges.

A subgraph of a graph is some set of the graph vertices and some set of the graph edges. At that, the set of edges must meet the condition: both ends of each edge from the set must belong to the chosen set of vertices.

Your task is to find a *p*-interesting graph consisting of *n* vertices.

Input

The first line contains a single integer *t* (1 ≤ *t* ≤ 5) — the number of tests in the input. Next *t* lines each contains two space-separated integers: *n*, *p* (5 ≤ *n* ≤ 24; *p* ≥ 0; ) — the number of vertices in the graph and the interest value for the appropriate test.

It is guaranteed that the required graph exists.

Output

For each of the *t* tests print 2*n* + *p* lines containing the description of the edges of a *p*-interesting graph: the *i*-th line must contain two space-separated integers *a*_{i}, *b*_{i} (1 ≤ *a*_{i}, *b*_{i} ≤ *n*; *a*_{i} ≠ *b*_{i}) — two vertices, connected by an edge in the resulting graph. Consider the graph vertices numbered with integers from 1 to *n*.

Print the answers to the tests in the order the tests occur in the input. If there are multiple solutions, you can print any of them.

Examples

Input

1

6 0

Output

1 2

1 3

1 4

1 5

1 6

2 3

2 4

2 5

2 6

3 4

3 5

3 6

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

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