Average Counting - Repovive Goodbye 2025 Round | Repovive

1A. Average Counting

500 pts2s256 MB

You are given three integers $l$ , $r$ , and $x$ .

Count the number of pairs $(a,b)$ such that $l \le a \le b \le r$ and the arithmetic mean of $a$ and $b$ is equal to $x$ , i.e. $\frac{a+b}{2} = x$ .

Constraints

$1 \le t \le 10^5$
$1 \le l \le r \le 2 \times 10^9$
$1 \le x \le 10^9$

Input

t \\[0.5em] \left. \begin{array}{l} l \quad r \quad x \end{array} \right\} \times t

Output

\left. \begin{array}{l} ans \end{array} \right\} \times t

Samples

Input

Case 1

1 5 3

Case 2

1 5 1

Case 3

1 5 10

Case 4

7 7 7

Explanation

Case 1

$l=1$ , $r=5$ , $x=3$

We need pairs $(a,b)$ with $1 \le a \le b \le 5$ and $\frac{a+b}{2}=3$ , i.e., $a+b=6$ . Valid pairs: $(1,5), (2,4), (3,3)$ . Answer: 3.

Case 2

$l=1$ , $r=5$ , $x=1$

We need $a+b=2$ with $1 \le a \le b \le 5$ . Only valid pair: $(1,1)$ . Answer: 1.

Output

Case 1

Case 2

Case 3

Case 4

You are given three integers $l$ , $r$ , and $x$ .

Count the number of pairs $(a,b)$ such that $l \le a \le b \le r$ and the arithmetic mean of $a$ and $b$ is equal to $x$ , i.e. $\frac{a+b}{2} = x$ .

Constraints

$1 \le t \le 10^5$
$1 \le l \le r \le 2 \times 10^9$
$1 \le x \le 10^9$

t \\[0.5em] \left. \begin{array}{l} l \quad r \quad x \end{array} \right\} \times t

\left. \begin{array}{l} ans \end{array} \right\} \times t

$l=1$ , $r=5$ , $x=3$

We need pairs $(a,b)$ with $1 \le a \le b \le 5$ and $\frac{a+b}{2}=3$ , i.e., $a+b=6$ . Valid pairs: $(1,5), (2,4), (3,3)$ . Answer: 3.

$l=1$ , $r=5$ , $x=1$

We need $a+b=2$ with $1 \le a \le b \le 5$ . Only valid pair: $(1,1)$ . Answer: 1.

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1A. Average Counting

Input

Output

Samples

1A. Average Counting

Constraints

Input

Output

Samples

Constraints