You are given two integers $$$x$$$ and $$$y$$$. A sequence $$$a$$$ of length $$$n$$$ is called modular if $$$a_1=x$$$, and for all $$$1 \lt i \le n$$$ 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.

Input

Each 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 $$$2 \cdot 10^5$$$.

Output

For 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.

Note

In 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.

Modular Sequence

Examples