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:

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

Input

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 $$$2 \cdot 10^5$$$.

Output

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

Note

In the first case, you can proceed as follows:

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

The Humanoid

Examples