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C. Little Girl and Maximum Sum

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe 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* ≤ 2·10^{5}) and *q* (1 ≤ *q* ≤ 2·10^{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 ≤ *a*_{i} ≤ 2·10^{5}) — 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

3 3

5 3 2

1 2

2 3

1 3

Output

25

Input

5 3

5 2 4 1 3

1 5

2 3

2 3

Output

33

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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