CF2051D Counting Pairs

You are given a sequence $ a $ , consisting of $ n $ integers, where the $ i $ -th element of the sequence is equal to $ a_i $ . You are also given two integers $ x $ and $ y $ ( $ x \le y $ ). A pair of integers $ (i, j) $ is considered interesting if the following conditions are met: - $ 1 \le i < j \le n $ ; - if you simultaneously remove the elements at positions $ i $ and $ j $ from the sequence $ a $ , the sum of the remaining elements is at least $ x $ and at most $ y $ . Your task is to determine the number of interesting pairs of integers for the given sequence $ a $ .

The first line contains one integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. Each test case consists of two lines: - The first line contains three integers $ n, x, y $ ( $ 3 \le n \le 2 \cdot 10^5 $ , $ 1 \le x \le y \le 2 \cdot 10^{14} $ ); - The second line contains $ n $ integers $ a_1, a_2, \dots, a_n $ ( $ 1 \le a_i \le 10^{9} $ ). Additional constraint on the input: the sum of $ n $ across all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, output one integer — the number of interesting pairs of integers for the given sequence $ a $ .

In the first example, there are $ 4 $ interesting pairs of integers: 1. $ (1, 2) $ ; 2. $ (1, 4) $ ; 3. $ (2, 3) $ ; 4. $ (3, 4) $ .