Ivan has $$$n$$$ types of items, with an infinite supply of each type. The weight of the $$$i$$$-th type of item is $$$w_i$$$.
Ivan wants to know whether it is possible to select exactly $$$n$$$ items such that the total weight of the selected items equals $$$m$$$.
Each test file contains multiple test cases. The first line contains the number of test cases $$$T$$$ ($$$1 \leq T \leq 10^4$$$). The description of the test cases follows.
The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \leq n \leq 10^5, 0 \leq m \leq n^2$$$).
The second line contains $$$n$$$ integers $$$w_1, w_2, \cdots, w_n$$$ ($$$0 \leq w_i \leq n$$$).
For each test file, it is guaranteed that the sum of all $$$n$$$ over all test cases does not exceed $$$10^5$$$.
For each test case, output "Yes" if the desired selection is possible; otherwise, output "No".
You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.
45 250 0 0 0 55 114 4 4 5 55 01 2 3 4 55 250 1 2 3 4
Yes No No No
In the first test case, you can select $$$5$$$ items of the $$$5$$$th type, with a total weight of $$$25$$$, so you output "Yes".
In the second test case, it can be proven that there is no selection of items that results in a total weight of $$$11$$$, so you output "No".
In the third test case, since you must select $$$5$$$ items and the weight of the lightest item is $$$1$$$, there is no way to select items with a total weight of $$$0$$$, so you output "No".
In the fourth test case, since the heaviest item weighs $$$4$$$, there is no way to select items with a total weight of $$$25$$$, so you output "No".
