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:</p>

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

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 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.

출력 형식

In the first n lines of the standard output 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.

예제 입력

8
4

예제 출력

0
1
2
1
0
-1
0
1