X Subarrays

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Binary Search, Algorithms
Problem

You are given an array \(A\) of length \(N\) sorted in non-decreasing order and an integer \(X\). Find the number of subarrays such that the sum of the minimum and maximum element of that subarray is less than or equal to \(X\).

Input Format:

  • The first line contains an integer \(T\), which denotes the number of test cases.
  • The first line of each test case contains two integers, \(N\) and \(X\).
  • The next line of each test case contains \(N\) space-separated integers, elements of array \(A\).

Output Format:

For each test case, print the number of subarrays such that the sum of the minimum and maximum element of that subarray is less than or equal to \(X\).

Constraints:

\(1 \leq T \leq 10 \\ 1 \leq N \leq 10^5 \\ 1 \leq A[i], X \leq 10^5\)

Time Limit: 1
Memory Limit: 256
Source Limit:
Explanation

For first test case:
Subarray is [3]. Hence, the answer is 1.

For second test case:
Subarrays are [1], [1, 3]. Hence, the answer is 2.

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