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Gauss - The Great Mathematician

By himuhasib · Limits 1s, 1.0 GB

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:

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

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

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

8,3,2,7,12,17,-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(1T103)T(1\leq T \leq 10^3) denoting the number of test cases. In the next TT lines, there will be 3 integers A1,A2,AnA_1, A_2, A_n where A1A_1 is the first term, A2A_2 is the second term and AnA_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:

1T1031 \leq T \leq 10^3

104A1<A2An104-10^4 \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.

Sample

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

Discussion

Statistics


98% Solution Ratio

fsshakkhorEarliest, Dec '18

fsshakkhorFastest, 0.0s

fsshakkhorLightest, 131 kB

touhidurrrShortest, 98B

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