Arithmetic Sequence (Hard)
Arithmetic Sequence is a sequence of numbers where the difference between two consecutive numbers are same. For example, the sequence 2, 4, 6, 8, 10, …. n is an arithmetic sequence where the difference between consecutive numbers is 2.
Carl Friedrich Gauss is known to be one of the best mathematician of all time. A story about his childhood goes like this: When Gauss was nine years old, his teacher asked him to add numbers from 1 to 100, thinking it would keep Gauss busy for a while. But Gauss came up with the answer very quickly instead. He found the following observation very helpful while solving the problem:
1 + 2 + 3 + 4 + 5 + …… + 100
100 + 99 + 98 + 97 + 96 + ……..+ 1
101 + 101 + 101 + 101 + 101 + ……. + 101
Since there are 100 terms each having the value of 101, the answer should be ( 100 * 101 ) / 2, because each number from 1 to 100 were added twice in this summation. So, if a person is given n, he can easily calculate the sum from 1 to n with a simple formula.
In this problem, you will be given an integer N, you will have to find the summation of integers from 1 to N. To make a the problem a bit more challenging, you will also be asked to subtract some of the numbers from this summation.
The first line contain an integer N ( 1 ≤ N ≤ 109 ), the length of the arithmetic sequence. The next line will contain an integer M ( 1 ≤ M ≤ min( N , 1000000 ) ), the amount of number that will be subtracted from the sequence. The following M lines will have one integer Mi (1 ≤ Mi ≤ N), the numbers that will be subtracted from the sequence. Each of these M numbers will be unique.
Output a single integer, the result of the arithmetic sequence after subtracting the given numbers.
3 1 3
3 2 1 2