Given two integers L and K, find the least integer R such that the number of set bits in the range [L, R] is at least K.

Here, "number of set bits" means the number of 1 bits in the binary representation of the integers.

Task

Find the minimum value of R

Example

Assumption:

Approach:

Input format

Note: This is the input format that you must use to provide custom input (available above the Compile and Test button)

Output format

For each test case, output one integer in a single line denoting the minimum value of R.

Constraints

\(1 \le T \le 20\)

\(1 \le L, K \le 10^{15}\)

Number of set bits in \([1, L-1]\) + K <= Number of set bits in \([1, 2*10^{15}]\)