#656 XOR Network

Statement

Statement language

There are $N$ vertices numbered from $0$ through $N-1$ . Choose a non-negative integer $t$ and construct an undirected graph by connecting two distinct vertices $i$ and $j$ with an edge if and only if $i\oplus j\leq t$ .

The symbol $\oplus$ denotes bitwise XOR. When the two numbers are written in binary, each bit of the result is $1$ if the corresponding bits differ and $0$ otherwise. For example, $3\oplus 5=6$ .

A connected component is a maximal set of vertices in which any two vertices can reach each other by following edges. An isolated vertex also forms a connected component.

Find the smallest non-negative integer $t$ for which the graph has at most $C$ connected components.

Input

The input is given in the following format.

$T$ $\mathrm{case}_1$ $\mathrm{case}_2$

Output

For each test case, output the smallest non-negative integer $t$ for which the graph has at most $C$ connected components, on a separate line. Output the answers in the order the test cases appear in the input.

Constraints

$1\leq T\leq 100\ 000$ .
$1\leq N,C\leq 10^9$ .

Subtasks

#	Score	Constraints
1	19	$N \leq 100$ .
2	27	$C=1$ .
3	54	No additional constraints.

Samples

Input

Output

When $t=0$ , the graph has no edges and therefore has $N$ connected components. In each of the first three test cases, $N\leq C$ , so the answer is $0$ . In each remaining test case, .