An arithmetic progression is a sequence of the form a, a+b, a+2b, ..., a+nb 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).
TIME LIMIT: 5 secs
PROGRAM NAME: ariprog
INPUT FORMAT
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.
SAMPLE INPUT (file ariprog.in)
5
7
OUTPUT FORMAT
If no sequence is found, a single 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.
An arithmetic progression is a sequence of the form a, a+b, a+2b, ..., a+nb 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).
TIME LIMIT: 5 secs PROGRAM NAME: ariprog INPUT FORMAT
SAMPLE INPUT (file ariprog.in) 5 7 OUTPUT FORMAT If no sequence is found, a single 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.
SAMPLE OUTPUT (file ariprog.out) 1 4 37 4 2 8 29 8 1 12 5 12 13 12 17 12 5 20 2 24