Statement

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.

Format

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.

Sample

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