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 ≤ l i ≤ r i ≤ 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.
Input
The first line contains two space-separated integers n (1 ≤ n ≤ 2·105) and q (1 ≤ q ≤ 2·105) — the number of elements in the array and the number of queries, correspondingly.
The next line contains n space-separated integers a i (1 ≤ a i ≤ 2·105) — the array elements.
Each of the following q lines contains two space-separated integers l i and r i (1 ≤ l i ≤ r i ≤ n ) — the i -th query.
Output
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 С++. It is preferred to use the cin, cout streams or the %I64d specifier.
Examples
Input
Copy
3 3
5 3 2
1 2
2 3
1 3
Output
Copy
25
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