1538C · Number of Pairs

Problem: You are given an array $a$ of $n$ integers. Find the number of pairs $(i, j)$ ($1 \le i < j \le n$) where the sum of $a_i + a_j$ is greater than or equal to $l$ and less than or equal to $r$ (that is, $l \le a_i + a_j \le r$).

For example, if $n = 3$, $a = [5, 1, 2]$, $l = 4$ and $r = 7$, then two pairs are suitable:

• $i=1$ and $j=2$ ($4 \le 5 + 1 \le 7$);
• $i=1$ and $j=3$ ($4 \le 5 + 2 \le 7$).

Input Format: The first line contains an integer $t$ ($1 \le t \le 10^4$). Then $t$ test cases follow.

The first line of each test case contains three integers $n, l, r$ ($1 \le n \le 2 \cdot 10^5$, $1 \le l \le r \le 10^9$) — the length of the array and the limits on the sum in the pair.

The second line contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$).

It is guaranteed that the sum of $n$ overall test cases does not exceed $2 \cdot 10^5$.

Output Format: For each test case, output a single integer — the number of index pairs $(i, j)$ ($i < j$), such that $l \le a_i + a_j \le r$.