Sum of one-sequence
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, ..., an] is a one-sequence if
- for any k, such that 1 <= k < n : |ak - ak+1| = 1 and
- a1 = 0
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
Sample input: 1 8 4</p>Sample output: 0 1 2 1 0 -1 0 1