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We say that a sequence of integers is a one-sequence if the difference between any two consecutive numbers in this sequence is or and its first element is . More precisely: is a one-sequence if:

- for any , such that : and
- .

Write a program that:

- reads two integers describing the length of the sequence and the sum of its elements, from the standard input;
- finds a one-sequence of the given length whose elements sum up to the given value or states that such a sequence does not exist;
- writes the result to the standard output.

In the first line of the standard input there is a number , such that , which is the number of elements in the sequence. In the second line there is a number , which is the sum of the elements of the sequence, such that .

In the first lines of the standard output there should be written integers (one in each line)
that are the elements of the sequence (-th element in the -th line) whose sum is
or the word `NIE` (which means “no” in Polish) if such a sequence does not exist.

For the input data:

8 4

the correct result is:

0 1 2 1 0 -1 0 1

*Task author: Grzegorz Jakacki.*