Problem Description

In the world of Tivat where Pink Rabbit resides, there are $n$ types of elements. Each element can contain a certain amount of energy, and different elements can react with each other.

Pink Rabbit has mastered these $n$ elements. Initially, the energy contained in each element he possesses is $a_1, a_2, \cdots, a_n$.

The details of reactions between different elements are as follows:

Reaction Condition: For any two elements $i, j$ ($i \neq j$), if $a_i \times a_j$ is a multiple of $154$ or $147$, they can react. Elements cannot react with themselves.
Reaction Result: Including these two elements, the energy of all $n$ elements doubles (i.e., all $a_i$ become twice their original value).
Reaction Frequency: There is no limit to the number of times any two elements can react (i.e., the same two elements, if they continue to meet the reaction condition, can react multiple times).

Now, Pink Rabbit wants to use elemental reactions to increase the total energy of his elements to be greater than or equal to $k$, in order to defeat the most powerful monster in the Tivat world—Devil. He wants to know if, after some number of reactions (including zero), $a_1 + a_2 + \cdots + a_n$ can be greater than or equal to $k$.

Input Format

There are multiple sets of data in a single test case.

The input consists of $2 \times T + 1$ lines.

The first line contains an integer $T$, representing the number of data sets.

For each set of data:
The first line contains two integers $n, k$, representing the number of element types and Pink Rabbit's target, respectively.
The second line contains $n$ integers $a_1, a_2, \cdots, a_n$, representing the initial energy values of each element.

Output Format

The output consists of $T$ lines.

For each set of data:
Output a single line containing a string. If Pink Rabbit can achieve $a_1 + a_2 + \cdots + a_n$ greater than or equal to $k$ through some number of reactions (including zero), output Yes, otherwise output No.

Sample Input and Output

Input Sample #1

1
4 1395
143 238 174 199

Output Sample #1

Yes

Input Sample #2

1
4 1441
677 293 859 751

Output Sample #2

Yes

Input Sample #3

1
4 1295
136 875 196 34

Output Sample #3

No

Notes

Sample 1 Explanation

First, Pink Rabbit can choose $143$ and $238$ to multiply, resulting in $143 \times 238 = 34034 = 154 \times 221$. At this point, all element energies double, becoming $286, 476, 348, 398$, and $286 + 476 + 348 + 398 = 1508 \geq 1395$, so Pink Rabbit can achieve the goal with one operation.

Sample 2 Explanation

$677 + 293 + 859 + 751 = 2580 \geq 1441$, so Pink Rabbit can achieve the goal without any operations.

Sample 3 Explanation

Pink Rabbit cannot trigger any elemental reactions, and the sum of the four energies is $< 1295$, so Pink Rabbit cannot achieve the goal.

Data Size and Constraints

Let $N = \sum n$, representing the total sum of $n$ across all test data in a single test case. Let $K$ represent the total length of $k$ across all test data in a single test case.

For $100\%$ of the data, it is guaranteed that $1 \leq T \leq 10^5$, $1 \leq n, N \leq 10^6$, $1 \leq k \leq 10^{10^5}$, $1 \leq a_i \leq 10^9$, $1 \leq K \leq 2 \times 10^6$.

见题面 Input 部分

见题面 Output 部分