[문제요약]M 개의 사탕이 있고 N 명의 아이들이 있다. N 명의 아이들이 요구하는 사탕수가 주어질 때 화(anger)의 합의 최소값을 구하는게 문제이다.

화(anger) = (사탕수 - 받은 사탕수)^2

가지고 있는 사탕수는 아이들의 원하는 사탕수의 합 보다는 항상 더 적다.

Each child has stated the number of candies that it wants. If a child isn’t given the amount of candy it wants, it will get angry. In fact it’ll get angrier for each candy it is deprived of. Some speculate that it’s anger will be equal to the square of the number of candy it is deprived of. For instance, if Mirko states that he wants 32 candies but receives only 29, he would be missing 3 candies, so his anger would be equal to 9.

Unfortunately, there is an insufficient amount of candy to satisfy all children. Therefore, the candies should be distributed in such a way that the sum of the children’s anger is minimal.

입력

• The first line contains two integers, M (1 <= M <= 2*10^9) and N (1 <= N <= 100 000).
• The following N lines contain integers (one per line) which represent the wishes of the children. Those numbers are all strictly less than 2*10^9, and their sum always exceeds M.

출력

입출력 예

입력

5 3
1
3
2

출력

1

입력

10 4
4
5
2
3

출력

4

출처:coci 2010