F. Zeros and Ones
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Let $$$S$$$ be the Thue-Morse sequence. In other words, $$$S$$$ is the $$$0$$$-indexed binary string with infinite length that can be constructed as follows:

  • Initially, let $$$S$$$ be "0".
  • Then, we perform the following operation infinitely many times: concatenate $$$S$$$ with a copy of itself with flipped bits.

    For example, here are the first four iterations:

    Iteration$$$S$$$ before iteration$$$S$$$ before iteration with flipped bitsConcatenated $$$S$$$
    10101
    201100110
    30110100101101001
    401101001100101100110100110010110
    $$$\ldots$$$$$$\ldots$$$$$$\ldots$$$$$$\ldots$$$

You are given two positive integers $$$n$$$ and $$$m$$$. Find the number of positions where the strings $$$S_0 S_1 \ldots S_{m-1}$$$ and $$$S_n S_{n + 1} \ldots S_{n + m - 1}$$$ are different.

Input

Each test contains multiple test cases. The first line of the input contains a single integer $$$t$$$ ($$$1 \le t \le 100$$$) — the number of test cases. The description of the test cases follows.

The first and only line of each test case contains two positive integers, $$$n$$$ and $$$m$$$ respectively ($$$1 \leq n,m \leq 10^{18}$$$).

Output

For each testcase, output a non-negative integer — the Hamming distance between the two required strings.

Example
Input
6
1 1
5 10
34 211
73 34
19124639 56348772
12073412269 96221437021
Output
1
6
95
20
28208137
48102976088
Note

The string $$$S$$$ is equal to 0110100110010110....

In the first test case, $$$S_0$$$ is "0", and $$$S_1$$$ is "1". The Hamming distance between the two strings is $$$1$$$.

In the second test case, $$$S_0 S_1 \ldots S_9$$$ is "0110100110", and $$$S_5 S_6 \ldots S_{14}$$$ is "0011001011". The Hamming distance between the two strings is $$$6$$$.