Note that the memory limit is unusual.

The Cheshire Cat has a riddle for Alice: given $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ and a target $$$m$$$, is there a way to insert $$$+$$$ and $$$\times$$$ into the circles of the expression $$$$$$a_1 \circ a_2 \circ \cdots \circ a_n = m$$$$$$ to make it true? We follow the usual order of operations: $$$\times$$$ is done before $$$+$$$.

Although Alice is excellent at chess, she is not good at math. Please help her so she can find a way out of Wonderland!

Input

Each test contains multiple test cases. The first line of input contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers $$$n, m$$$ ($$$1\le n\le 2\cdot 10^5$$$; $$$1\le m\le 10^4$$$) — the number of integers and the target, respectively.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0\le a_i\le 10^4$$$) — the elements of the array $$$a$$$.

The sum of $$$n$$$ over all test cases does not exceed $$$2\cdot 10^5$$$.

Output

For each test case, output "YES" without quotes if it is possible to get the target by inserting $$$+$$$ or $$$\times$$$ and "NO" otherwise.

You can output each letter in any case (for example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as a positive answer).

Note

Possible solutions for the first four test cases are shown below. $$$$$$\begin{align*} 2 \times 1 + 1 \times 1 \times 2 &= 4 \\ 2 \times 1 + 1 + 1 \times 2 &= 5 \\ 2 \times 1 + 1 + 1 + 2 &= 6 \\ 2 + 1 + 1 + 1 + 2 &= 7 \\ \end{align*}$$$$$$ It is impossible to get a result of $$$8$$$ in the fifth test case.

Alice's Adventures in Addition

Examples