Johann Carl Friedrich Gauß (1777 – 1855) was one of the most important German mathematicians. For those of you who remember the Deutsche Mark, a picture of him was printed on the 10 – DM bill. In elementary school, his teacher J. G. Büttner tried to occupy the pupils by making them add up the integers from 1 to 100. The young Gauß surprised everybody by producing the correct answers (5050) within seconds.
Can you write a computer program that can compute such sums really quickly?
Given two integers n and m, you should compute the sum of all the integers from n to m. In other words, you should compute
The first line contains the number of scenarios. Each scenario consists of a line containing the numbers n and m (−109 ≤ n ≤ m ≤ 109).
The output for every scenario begins with a line containing “Scenario #i:”, where i is the number of the scenario starting at 1. Then print the sum of all integers from n to m. Terminate the output for the scenario with a blank line.
3 1 100 -11 10 -89173 938749341
Scenario #1: 5050 Scenario #2: -11 Scenario #3: 440625159107385260