E. Modular Sequencetime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given two integers x and y. A sequence a of length n is called modular if a_1=x, and for all 1 < i \le n the value of a_{i} is either a_{i-1} + y or a_{i-1} \bmod y. Here x \bmod y denotes the remainder from dividing x by y.Determine if there exists a modular sequence of length n with the sum of its elements equal to S, and if it exists, find any such sequence.InputEach test contains multiple test cases. The first line contains the number of test cases t (1 \le t \le 2 \cdot 10^4). The description of the test cases follows.The first and only line of each test case contains four integers n, x, y, and s (1 \le n \le 2 \cdot 10^5, 0 \le x \le 2 \cdot 10^5, 1 \le y \le 2 \cdot 10^5, 0 \le s \le 2 \cdot 10^5) — the length of the sequence, the parameters x and y, and the required sum of the sequence elements.The sum of n over all test cases does not exceed 2 \cdot 10^5, and also the sum of s over all test cases does not exceed 2 \cdot 10^5.OutputFor each test case, if the desired sequence exists, output "Yes" on the first line (without quotes). Then, on the second line, output n integers a_1, a_2, \ldots, a_n separated by a space — the elements of the sequence a. If there are multiple suitable sequences, output any of them.If the sequence does not exist, output "No" on a single line.You can output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.ExampleInput
35 8 3 283 5 3 69 1 5 79Output
YES
8 11 2 2 5 
NO
NO
NoteIn the first example, the sequence [8, 11, 2, 5, 2] satisfies the conditions. Thus, a_1 = 8 = x, a_2 = 11 = a_1 + 3, a_3 = 2 = a_2 \bmod 3, a_4 = 5 = a_3 + 3, a_5 = 2 = a_4 \bmod 3.In the second example, the first element of the sequence should be equal to 5, so the sequence [2, 2, 2] is not suitable.
35 8 3 283 5 3 69 1 5 79
YES 8 11 2 2 5  NO NO 
['brute force', 'constructive algorithms', 'dp', 'graphs', 'greedy', 'math', 'number theory', '*2300']