E. The Humanoidtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputThere 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.InputThe 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.OutputFor each test case, in a separate line, print the maximum number of astronauts that a humanoid can absorb.ExampleInput
84 12 1 8 93 36 2 604 55 1 100 53 238 6 31 1124 612 12 36 1004 12 1 1 153 515 1 13Output
4
3
3
3
0
4
4
3
NoteIn 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 
84 12 1 8 93 36 2 604 55 1 100 53 238 6 31 1124 612 12 36 1004 12 1 1 153 515 1 13
4 3 3 3 0 4 4 3 
['brute force', 'dp', 'sortings', '*1500']