I found an interesting problem on https://codeforces.com/problemset/problem/276/C:
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 ≤ 2·10^5) 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

I tried it in Python, but could not do it. Can you solve it?
n, q = map(int, input().split())
t = [0] + list(map(int, input().split()))
p = [0] * (n + 1)

for i in range(q):
    l, r = map(int, input().split())
    p[l - 1] += 1
    p[r] -= 1

for i in range(1, n + 1):
    p[i] += p[i - 1]

t.sort()
p.sort()

j = 0
while p[j] == 0: j += 1

print(sum(p[i] * t[i] for i in range(j, n + 1)))