Range Sum Frequency

You are given an array of integers and a list of query ranges. For each range query, calculate how many times the sum of the numbers within that range occurs among all subarrays of the given array. Your solution should efficiently compute results without re-evaluating sums for overlapping ranges. Input: - The first line contains two integers n and q (1 ≤ n ≤ 100,000, 1 ≤ q ≤ 100,000), the size of the array and the number of queries, respectively. - The second line contains n integers a[i] (1 ≤ a[i] ≤ 10000) representing the elements of the array. - The following q lines each contain two integers l and r (1 ≤ l ≤ r ≤ n), the inclusive bounds of the queries. Output: - For each query, output a single integer indicating the frequency of the subarray sum corresponding to the given range. Example: Input: 5 2 1 2 3 4 5 1 3 2 4 Output: 1 1