CF1759E.The Humanoid

There are $n$ astronauts working on some space station. An astronaut with the number $i$ ( $1 \le i \le n$ ) has power $a_i$ .

An evil humanoid has made his way to this space station. The power of this humanoid is equal to $h$ . Also, the humanoid took with him two green serums and one blue serum.

In one second , a humanoid can do any of three actions:

1. to absorb an astronaut with power strictly less humanoid power;
2. to use green serum, if there is still one left;
3. to use blue serum, if there is still one left.

When an astronaut with power $a_i$ is absorbed, this astronaut disappears, and power of the humanoid increases by $\lfloor \frac{a_i}{2} \rfloor$ , that is, an integer part of $\frac{a_i}{2}$ . For example, if a humanoid absorbs an astronaut with power $4$ , its power increases by $2$ , and if a humanoid absorbs an astronaut with power $7$ , its power increases by $3$ .

After using the green serum, this serum disappears, and the power of the humanoid doubles, so it increases by $2$ times.

After using the blue serum, this serum disappears, and the power of the humanoid triples, so it increases by $3$ times.

The humanoid is wondering what the maximum number of astronauts he will be able to absorb if he acts optimally.

The first line of each test contains an integer $t$ ( $1 \le t \le 10^4$ ) — number of test cases.

The first line of each test case contains integers $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — number of astronauts and $h$ ( $1 \le h \le 10^6$ ) — the initial power of the humanoid.

The second line of each test case contains $n$ integers $a_i$ ( $1 \le a_i \le 10^8$ ) — powers of astronauts.

It is guaranteed that the sum of $n$ for all test cases does not exceed $2 \cdot 10^5$ .

For each test case, in a separate line, print the maximum number of astronauts that a humanoid can absorb.

In the first case, you can proceed as follows:

1. use green serum. $h = 1 \cdot 2 = 2$
2. absorb the cosmonaut $2$ . $h = 2 + \lfloor \frac{1}{2} \rfloor = 2$
3. use green serum. $h = 2 \cdot 2 = 4$
4. absorb the spaceman $1$ . $h = 4 + \lfloor \frac{2}{2} \rfloor = 5$
5. use blue serum. $h = 5 \cdot 3 = 15$
6. absorb the spaceman $3$ . $h = 15 + \lfloor \frac{8}{2} \rfloor = 19$
7. absorb the cosmonaut $4$ . $h = 19 + \lfloor \frac{9}{2} \rfloor = 23$