# Practice on Toph

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# 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.

## Input

The first line contain an integer **N** **( 1 ≤ N ≤ 10 ^{9} )**, 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

**M**

_{i}**(1 ≤ M**, the numbers that will be subtracted from the sequence. Each of these

_{i}≤ N)**M**numbers will be

**unique**.

## Output

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

## Samples

Input | Output |
---|---|

3 1 3 | 3 |

Input | Output |
---|---|

3 2 1 2 | 3 |

93% Solution Ratio

aminulEarliest,

arnob_daFastest, 0.0s

fsshakkhorLightest, 131 kB

mdvirusShortest, 109B

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