Interesting Set

Mr.Frog is researching integers.

He converts two integers X and Y into binary without leading zeros, if they have the same quantity of 0
and the same quantity of 1 in the binary, Mr.Frog will think these two integers are friendly.
For example, 5₍₁₀₎ = 101₍₂₎ and 6₍₁₀₎ = 110₍₂₎, both of them have two 1 and one 0 in the binary, so
Mr.Frog thinks 5 and 6 are friendly.
Now, Mr.frog gets an integer N and defines a sorted set S. The sorted set S consists of integers which
are friendly with N and bigger than N. He wants to know what is the K^th integer in S.
Because Mr.Frog is on his way back from Hong Kong to Beijing, he wants to ask you for help.

The first line contains an integer T, where T is the number of test cases. T test cases follow.

For each test case, the only line contains tow integers N and K.

1<=T<=200

1<=N<=10¹⁸

1<=K<=10¹⁸

For each test case, print one line containing “Case #x: y”, where x is the test case number (starting
from 1) and y is the K^th integer in the sorted set S. If the integer he wants to know does not exist, y is
“IMPOSSIBLE”.

2
9 2
7 4

Case #1: 12
Case #2: IMPOSSIBLE

For the first case, the sorted set S will be {10,12}, so the 2^nd integer is 12.
For the second case, the sorted set S will be ∅, so the answer is “IMPOSSIBLE”.