10119_ArithmeticProgressions

An arithmetic progression is a sequence of the form a, a+b, a+2b, ..., a+n×b where n = 0, 1, 2, 3, ... . For this problem, a is a non-negative integer and b is a positive integer.

Write a program that finds all arithmetic progressions of length n in the set S of bisquares. The set of bisquares is defined as the set of all integers of the form p² + q² (where p and q are non-negative integers).

Multi test cases. Each case has two lines :

Line 1:  N (3 ≤ N ≤ 25), the length of progressions for which to search

Line 2:  M (1 ≤ M ≤ 250), an upper bound to limit the search to the bisquares with 0 ≤ p, q ≤ M.

For each case :

If no sequence is found, a singe line reading 'NONE'. Otherwise, output one or more lines, each with two integers: the first element in a found sequence and the difference between consecutive elements in the same sequence. The lines should be ordered with smallest-difference sequences first and smallest starting number within those sequences first.

There will be no more than 10,000 sequences.

After each case , output a blank line.

5
7

3
2

1 4
37 4
2 8
29 8
1 12
5 12
13 12
17 12
5 20
2 24

0 1
0 2
2 3
0 4