COCI '14 Contest 1 #1 Prosjek

Points: 5 (partial)

Time limit: 1.0s

Memory limit: 32M

Problem type

Mirko is practicing arithmetic operations in an interesting way during math class. First, he writes a sequence of integers $A$ $A$ . Then, underneath the first sequence, he writes another sequence of integers $B$ $B$ which he gets by replacing every number from the sequence $A$ $A$ with the average value of all the numbers before the current one, including it.

For example, if the first sequence of integers $A$ $A$ is equal to

$\displaystyle 1, 3, 2, 6, 8$ $1, 3, 2, 6, 8$

then the second sequence of integers $B$ $B$ is going to be

$\displaystyle \frac 1 1, \frac{1+3} 2, \frac{1+3+2} 3, \frac{1+3+2+6} 4, \frac{1+3+2+6+8} 5$ $\frac{1}{1}, \frac{1 + 3}{2}, \frac{1 + 3 + 2}{3}, \frac{1 + 3 + 2 + 6}{4}, \frac{1 + 3 + 2 + 6 + 8}{5}$

in other words

$\displaystyle 1, 2, 2, 3, 4$ $1, 2, 2, 3, 4$

You are given the second sequence of integers $B$ $B$ . Determine the first sequence of integers $A$ $A$ to check Mirko's calculations.

Input

The first line of input contains the integer $N$ $N$ $(1 \le N \le 100)$ $(1 \leq N \leq 100)$ , the length of sequence $B$ $B$ .
The second line of input contains the sequence of $N$ $N$ space-separated integers $B_i$ $B_{i}$ $(1 \le B_i \le 10^9)$ $(1 \leq B_{i} \leq 10^{9})$ .

Output

The first and only line of output must contain a sequence of $N$ $N$ space-separated integers $A_i$ $A_{i}$ .
Please note: The input data will be such that the elements from the sequence $A$ $A$ are integers $(1 \le A_i \le 10^9)$ $(1 \leq A_{i} \leq 10^{9})$ .

Sample Input 1

Copy

1
2

Sample Output 1

Copy

Sample Input 2

Copy

4
3 2 3 5

Sample Output 2

Copy

3 1 5 11

Sample Input 3

Copy

5
1 2 2 3 4

Sample Output 3

Copy

1 3 2 6 8

Explanation of Output for Sample Input 3

Look at the task description.

Comments

0

EdwinYang commented on Aug. 12, 2020, 5:30 p.m.

Are the example outputs wrong? for the second output, would the integers not be 3, (3+2)/2, (3+2+3)/3, (3+2+3+5)/4? So 3, 2.5, 8/3, 13/4?

1

maxcruickshanks commented on Aug. 12, 2020, 9:11 p.m.

No, the example outputs do not contain errors; you are trying to obtain an array that would result in sample input if you performed the above operation.

0

EdwinYang commented on Aug. 12, 2020, 9:29 p.m.

Oh I'm sorry you're working backwards. Thanks