13045번 - Elimination Round, Problem F 다국어

Gnome Paul is participating in the elimination round of Gnome Math Cup. Problem F is the following.

You are given n positive integers a₁, a₂, ..., a_n and a positive integer d. You have to find non-zero integers x₁, x₂, ..., x_n such that a₁·x₁ + a₂·x₂ + ... + a_n·x_n = d. Gnomes don't like big numbers, so a_i and d don't exceed 10⁶, and x_i must be between -10⁶ and 10⁶, but not equal to 0.

Help Paul to find at least one required sequence x₁, x₂, ..., x_n, or detect that there is no solution.

The first line of input contains t — the number of test cases. Tests follow.

The first line of each test contains two integers n and d (1 ≤ n ≤ 10⁵, 1 ≤ d ≤ 10⁶). The second line contains n integers a_i (1 ≤ a_i ≤ 10⁶). The sum of values of n for all test cases doesn't exceed 10⁵.

Print the answer for each test case. If the required sequence of x_i exists, print "YES" as the first line of output. The second line must contain the sequence itself. If there is no such sequence, output "NO" as the only line of output for this test.