We say that a sequence of integers is a one-sequence if the difference between any two consecutive numbers in this sequence is 1 or -1 and its first element is 0. More precisely: [a₁,a₂,...,a_n] is a one-sequence if

• for any k, such that 1<=k< n : |a_k-a_k+1| =1 and
• a₁=0

Task
Write a program that:

• reads two integers describing the length of the sequence and the sum of its elements, from the text file SUM.IN;
• 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 text file SUM.OUT.

Input
In the first line of the text file SUM.IN there is a number n, such that 1<=n<=10 000, which is the number of elements in the sequence. In the second line there is a number S, which is the sum of the elements of the sequence, such that |S| <= 50 000 000.

Output
In the first n lines of the text file SUM.OUT there should be written n integers (one in each line) that are the elements of the sequence (k-th element in the k-th line) whose sum is S or the word NIE (which means NO in Polish) if such a sequence does not exist.

Example
For the input file SUM.IN:

8
4

0
1
2
1
0
-1
0
1