Assembly via Remainders
Description
You are given an array $x_2,x_3,\dots,x_n$. Your task is to find any array $a_1,\dots,a_n$, where:
- $1\le a_i\le 10^9$ for all $1\le i\le n$.
- $x_i=a_i \bmod a_{i-1}$ for all $2\le i\le n$.
Here $c\bmod d$ denotes the remainder of the division of the integer $c$ by the integer $d$. For example $5 \bmod 2 = 1$, $72 \bmod 3 = 0$, $143 \bmod 14 = 3$.
Note that if there is more than one $a$ which satisfies the statement, you are allowed to find any.
The first line contains a single integer $t$ $(1\le t\le 10^4)$ — the number of test cases.
The first line of each test case contains a single integer $n$ $(2\le n\le 500)$ — the number of elements in $a$.
The second line of each test case contains $n-1$ integers $x_2,\dots,x_n$ $(1\le x_i\le 500)$ — the elements of $x$.
It is guaranteed that the sum of values $n$ over all test cases does not exceed $2 \cdot 10^5$.
For each test case output any $a_1,\dots,a_n$ ($1 \le a_i \le 10^9$) which satisfies the statement.
Input
The first line contains a single integer $t$ $(1\le t\le 10^4)$ — the number of test cases.
The first line of each test case contains a single integer $n$ $(2\le n\le 500)$ — the number of elements in $a$.
The second line of each test case contains $n-1$ integers $x_2,\dots,x_n$ $(1\le x_i\le 500)$ — the elements of $x$.
It is guaranteed that the sum of values $n$ over all test cases does not exceed $2 \cdot 10^5$.
Output
For each test case output any $a_1,\dots,a_n$ ($1 \le a_i \le 10^9$) which satisfies the statement.
5
4
2 4 1
3
1 1
6
4 2 5 1 2
2
500
3
1 5
3 5 4 9
2 5 11
5 14 16 5 11 24
501 500
2 7 5
Note
In the first test case $a=[3,5,4,9]$ satisfies the conditions, because:
- $a_2\bmod a_1=5\bmod 3=2=x_2$;
- $a_3\bmod a_2=4\bmod 5=4=x_3$;
- $a_4\bmod a_3=9\bmod 4=1=x_4$;