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.

有 $n$ 名宇航员在某空间站工作。编号为 $i$（$1 \le i \le n$）的宇航员拥有力量值 $a_i$。

一名邪恶的人形生物已潜入该空间站。该人形生物当前的力量值为 $h$，且随身携带两支绿色血清和一支蓝色血清。

每秒钟，该人形生物可执行以下三种操作之一：

1. 吸收一名力量值严格小于自身当前力量值的宇航员；
2. 使用一支绿色血清（前提是尚存至少一支）；
3. 使用一支蓝色血清（前提是尚存至少一支）。

当人形生物吸收一名力量值为 $a_i$ 的宇航员时，该宇航员消失，而人形生物的力量值增加 $\lfloor \frac{a_i}{2} \rfloor$，即 $\frac{a_i}{2}$ 的整数部分。例如：若吸收力量值为 $4$ 的宇航员，则力量值增加 $2$；若吸收力量值为 $7$ 的宇航员，则力量值增加 $3$。

使用绿色血清后，该血清被消耗，人形生物的力量值变为原来的 2 倍。

使用蓝色血清后，该血清被消耗，人形生物的力量值变为原来的 3 倍。

该人形生物想知道：若采取最优策略，最多能吸收多少名宇航员？

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 $2 \cdot 10^5$.

每组测试数据的第一行包含一个整数 $t$（$1 \le t \le 10^4$）—— 测试用例的数量。

每个测试用例的第一行包含两个整数 $n$（$1 \le n \le 2 \cdot 10^5$）—— 宇航员的数量，以及 $h$（$1 \le h \le 10^6$）—— 类人生物的初始能量值。

每个测试用例的第二行包含 $n$ 个整数 $a_i$（$1 \le a_i \le 10^8$）—— 各宇航员的能量值。

保证所有测试用例的 $n$ 值之和不超过 $2 \cdot 10^5$。

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

对于每个测试用例，在单独一行中输出一个人形生物最多能吸收的宇航员数量。

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 $4$. $h = 19 + \lfloor \frac{9}{2} \rfloor = 23$

在第一种情况下，你可以按如下步骤进行：

1. 使用绿色血清。$h = 1 \cdot 2 = 2$
2. 吸收宇航员 $2$。$h = 2 + \lfloor \frac{1}{2} \rfloor = 2$
3. 使用绿色血清。$h = 2 \cdot 2 = 4$
4. 吸收宇航员 $1$。$h = 4 + \lfloor \frac{2}{2} \rfloor = 5$
5. 使用蓝色血清。$h = 5 \cdot 3 = 15$
6. 吸收宇航员 $3$。$h = 15 + \lfloor \frac{8}{2} \rfloor = 19$
7. 吸收宇航员 $4$。$h = 19 + \lfloor \frac{9}{2} \rfloor = 23$