Sum of One-sequence

Memory limit: 32 MB

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
• .

Task

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.

Input

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 .

Output

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.

Example

For the input data:

8
4

the correct result is:

0
1
2
1
0
-1
0
1

Task author: Grzegorz Jakacki.