Assessment Disruption

It is finally time to submit your essays on economics for assessment!

Each essay is characterised by its word count  and its quality .
The required word count is , so the closer  to  is in your essay, the better mark you may expect.
And, surely, the higher the quality, the better. However, one essay can have a better quality and a bigger deviation from  than another,
so it is not clear which one is better.

As an economics student, you may know that this kind of situation is captured by Pareto dominance. Formally, essay  is said to dominate essay  in the Pareto sense
if , , and at least one of these inequalities is strict.

The professor is known to use this relation to mark the essays. First, she finds all the best essays: those that are not dominated by any other essay. These essays receive the same mark, which is the highest among this year's students (but still can fall below their expectations!).
Then she removes the marked essays and repeats the procedure, but the mark will be lower this time, and so on. More precisely, she uses the following algorithm:
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    All the essays are numbered from 1 to .
    Each essay can be either in work, postponed, or marked. Initially, all essays are in work.
    A variable  captures the rank of an essay, the lower, the better. Initially, .
    While there are any essays that are in work:
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        Iterate over all essay numbers from 1 to . If the -th essay is in work:
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            Iterate over all essay numbers from  to . If the -th essay is in work, compare essays  and  for dominance:
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                If  dominates , turn  into postponed.
                If  dominates , turn  into postponed and break the loop.
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            If the -th essay is still in work, it receives rank  and turns into marked.
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        All postponed essays become in work again.
        The rank is increased: .
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You are afraid that you, and everyone else, will get low marks, but someone told you that if it took the professor too long to perform the entire assessment,
the department would take it over, and the final marks would be based on a simple multiple-choice quiz.
By rigorous computations you found out that the number of essay comparisons should be at least  for this to happen.
Find the way to disrupt the assessment procedure.

Input

The first and only line of the input file contains two numbers,   and  , separated by a whitespace.

Output

Output  lines.
The -th line, , should contain the word count  and the quality  of the -th essay.
They should be integers that satisfy  and .
No two essays should be described by the same pair of numbers, because this counts as collusion, which you would want to avoid at all costs.
