# Practice on Toph

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# Arithmetic Sequence (Hard)

Limits 1s, 512 MB

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.

## Input

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

Output a single integer, the result of the arithmetic sequence after subtracting the given numbers.

## Samples

InputOutput
3
1
3
3
InputOutput
3
2
1
2
3

### Statistics

94% Solution Ratio

subintra2016.8$8KpTbEarliest, Nov '16 habib036Fastest, 0.0s subintra2016.8$8KpTbLightest, 131 kB

joe.masterShortest, 80B