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

Task

Write a program that for each test case:

• reads two integers describing the length of the sequence and the sum of its elements;
• 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

The number of test cases t is in the first line of input, then t test cases follow separated by an empty line.

In the first line of a test case 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

For each test case there should be written n integers (each integer in a separate line) that are the elements of the sequence (k-th element in the k-th line) whose sum is S or the word "No" if such a sequence does not exist. If there is more than one solution your program should output any one.

Consequent test cases should by separated by an empty line.

Example

Input:
1
8
4

Output:
0
1
2
1
0
-1
0
1