UVa 10014 Simple Calculations (mathematics)

10014-simple calculations

Time limit:3.000 seconds

Http://uva.onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&category=99&page=show_problem &problem=955

The Problem

There is a sequence of n+2 elements a₀, a₁,..., a_n+1 (n <= 3000; -1000 <= a_i 1000 ). It is known so a_i = (a_i–1 + a_i+1)/2–c_i for each i=1, 2, ..., N. You are given a₀, a_n+1, c₁, ..., c_n. Write a program which calculates a₁.

The Input

The the number of test cases, followed by a blank line.

For the all test case, the ' the ' a input file contains an integer n. The next two lines consist of numbers a₀ and a_n+1 each have two digits after decimal point, and the NE XT n lines contain numbers C_I (also with two digits after decimal point), one number per line.

Each test case is separated by a.

The Output

For each test case, the output file should contain a₁ in the same format as a₀ and a_n+1.

Print a blank line between the outputs for two consecutive test cases.

Sample Input

1

1
50.50
25.50
10.15

Sample Output

27.85

Ideas: