C. Little Girl and Maximum Sum
data structures; greedy; implementation; sortings
The little girl loves the problems on array queries very much.One day she came across a rather well-known problem: you've got an array of \(n\) elements (the elements of the array are indexed starting from 1); also, there are \(q\) queries, each one is defined by a pair of integers \(l_i\), \(r_i\) \((1 \le l_i \le r_i \le n)\). You need to find for each query the sum of elements of the array with indexes from \(l_i\) to \(r_i\), inclusive.The little girl found the problem rather boring. She decided to reorder the array elements before replying to the queries in a way that makes the sum of query replies maximum possible. Your task is to find the value of this maximum sum.
The first line contains two space-separated integers \(n\) (\(1 \le n \le 2\cdot10^5\)) and \(q\) (\(1 \le q \le 2\cdot10^5\)) — the number of elements in the array and the number of queries, correspondingly.The next line contains \(n\) space-separated integers \(a_i\) (\(1 \le a_i \le 2\cdot10^5\)) — the array elements.Each of the following \(q\) lines contains two space-separated integers \(l_i\) and \(r_i\) (\(1 \le l_i \le r_i \le n\)) — the \(i\)-th query.
In a single line print, a single integer — the maximum sum of query replies after the array elements are reordered.Please, do not use the %lld specifier to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specifier.