Daniel loves graphs. He thinks a graph is special if it has the following properties:
It is undirected.
The length of each edge is .
It includes exactly different lovely triplets.
A triplet is a set of different nodes. A triplet is lovely if the minimum distance between each pair of nodes in the triplet is exactly . Two triplets are different if or more of their component nodes are different.
Given and , help Daniel draw a special graph.
A single line containing space-separated integers, (the number of different lovely triplets you must have in your graph) and (the required distance between each pair of nodes in a lovely triplet), respectively.
For the first line, print space-separated integers, (the number of nodes in the graph) and (the number of edges in the graph), respectively.
On each line of the subsequent lines, print two space-separated integers, and , describing an edge between nodes and .
Your output must satisfy the following conditions:
If there is more than one correct answer, print any one of them.
There are exactly lovely triplets in this graph: , , and .
Observe that each node in a lovely triplet is edges away from the other nodes composing the lovely triplet.