CF1538C Number of Pairs

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 $ ).

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 $ .

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 $ .