Let's consider the 32 bit representation of all integers i from m up to n inclusive (m ≤ i ≤ n; m × n ≥ 0, -2³¹ ≤ m ≤ n ≤ 2³¹-1). Note that a negative number is represented in 32 bit Additional Code. That is the 32 bit sequence, the binary sum of which and the 32 bit representation of the corresponding positive number is 2³² (1 0000 0000 0000 0000 0000 0000 0000 0000 in binary).

For example, the 32 bit representation of 6 is 0000 0000 0000 0000 0000 0000 0000 0110 and the 32 bit representation of -6 is 1111 1111 1111 1111 1111 1111 1111 1010 because

    0000 0000 0000 0000 0000 0000 0000 0110 (6)
  + 1111 1111 1111 1111 1111 1111 1111 1010 (-6)
 ------------------------------------------
= 1 0000 0000 0000 0000 0000 0000 0000 0000 (232)

Let's sort the 32 bit representations of these numbers in increasing order of the number of bit 1. If two 32 bit representations that have the same number of bit 1, they are sorted in lexicographical order.

For example, with m = 0 and n = 5, the result of the sorting will be:

with m = -5 and n = -2, the result of the sorting will be:

Given m, n and k (1 ≤ k ≤ min{n − m + 1, 2 147 473 547}), your task is to write a program to find a number corresponding to k-th representation in the sorted sequence.

Input

The input consists of several data sets. The first line of the input file contains the number of data sets which is a positive integer and is not bigger than 1000. The following lines describe the data sets.

For each data set, the only line contains 3 integers m, n and k separated by space.

Output

For each data set, write in one line the k-th number of the sorted numbers.

Example

Input:
2
0 5 3
-5 -2 2

Output:
2
-5