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 $