Problem Statement

There is a tree with N vertices numbered 1 to N.
For each i\ $(2 \leq i \leq N),$ there is an edge connecting vertex i and vertex $\lfloor \frac{i}{2} \rfloor$.
There are no other edges.
In this tree, find the number of vertices whose distance from vertex X is K.
Here, the distance between two vertices u and v is defined as the number of edges in the simple path connecting vertices u and v.
You have T test cases to solve.

Input

The input is given from Standard Input in the following format, where $\mathrm{test}_i$ represents the i-th test case:
T
$\mathrm{test}_1$
$\mathrm{test}_2$
$\vdots$
$\mathrm{test}_T$

Each test case is given in the following format:
N X K

Output

Print T lines.
The $i-th line (1 \leq i \leq T)$ should contain the answer to the i-th test case as an integer.

Constraints

• $1\leq T \leq 10^5$
• $1\leq N \leq 10^{18}$
• $1\leq X \leq N$
• $0\leq K \leq N-1$
• All input values are integers.

Sample Input 1

5
10 2 0
10 2 1
10 2 2
10 2 3
10 2 4

Sample Output 1

1
3
4
2
0

The tree for N=10 is shown in the following figure.

Here,

• There is 1 vertex, 2, whose distance from vertex 2 is 0.
• There are 3 vertices, 1,4,5, whose distance from vertex 2 is 1.
• There are 4 vertices, 3,8,9,10, whose distance from vertex 2 is 2.
• There are 2 vertices, 6,7, whose distance from vertex 2 is 3.
• There are no vertices whose distance from vertex 2 is 4.

Sample Input 2

10
822981260158260522 52 20
760713016476190629 2314654 57
1312150450968417 1132551176249851 7
1000000000000000000 1083770654 79
234122432773361868 170290518806790 23
536187734191890310 61862 14
594688604155374934 53288633578 39
1000000000000000000 120160810 78
89013034180999835 14853481725739 94
463213054346948152 825589 73

Sample Output 2

1556480
140703128616960
8
17732923532771328
65536
24576
2147483640
33776997205278720
7881299347898368
27021597764222976

见题面 Input 部分

见题面 Output 部分