1627: Gauß in Elementary School

Johann Carl Friedrich Gau? (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. B¨uttner tried to occupy the pupils by making them add up the integers from 1 to 100. The young Gau? 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 m Xi=n

The first line contains the number of scenarios. Each scenario consists of a line containing the numbers n and m (-10^1000 <= n <= m <= 10^1000).

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