# Practice on Toph

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# Gauss - The Great Mathematician

**Carl Friedrich Gauss** was a great mathematician. When he was a child, his teacher told him to sum up all the numbers from 1 to 100 to keep him busy for some time. To his surprise, Gauss solved the problem in a few moments. He contributed in many fields of science. Some of his contributions are used in Computer Science too! #Respect!

In this problem, we want to keep you busy too! You have to find the sum of an arithmetic sequence. In mathematics, an arithmetic sequence is a sequence of numbers such that the difference between two consecutive terms is constant.

**Example:**

`$1, 2, 3, 4, 5, 6, \cdots $`

`$2, 7, 12, 17, 22, 27, \cdots $`

`$27, 22, 17, 12, 7, 2, -3, -8, \cdots $`

`$-8, -3, 2, 7, 12, 17, \cdots $`

But in this problem, we are only interested in **increasing arithmetic sequence** where each term is greater than the previous term. You will be given the first two terms and the last term of an **increasing arithmetic sequence**. You have to find the sum of all the terms of the given sequence.

## Input

The first line of the input will only contain a single integer `$T(1\leq T \leq 10^3)$`

denoting the number of test cases. In the next `$T$`

lines, there will be 3 integers `$A_1, A_2, A_n$`

where `$A_1$`

is the first term, `$A_2$`

is the second term and `$A_n$`

is the last term of the sequence. It is guaranteed that a valid sequence of integers can be formed from the given 3 integers.

#### Constraints:

`$1 \leq T \leq 10^3$`

`$-10^4 \leq A_1 < A_2 \leq A_n \leq 10^4$`

## Output

For each test case, print the sum of the sequence in a single line.

## Samples

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

4 1 2 6 -6 -5 -1 2 7 22 -8 -3 17 | 21 -21 60 27 |

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