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Number Crafting

By ahmed_redwan · Limits 1s, 512 MB

Game is one type of competency, and when it befalls by any number its really astonish.

Rifat is very good in mathematics and he always play with numbers . He take few numbers M and sum up on it. Morever he divides the sum up number by the least number of them.

And at a time he become so exhausted. So, your task is to help him. Note Rifat always keep the integer part.

Input

The input consists of several test case T (max 50). The first line of each test Case take a number N (1 ≤ N ≤ 10000). which will illustrate how many number you want to take. The next line contains N integers M (1 ≤ M ≤ 500) separated by spaces.

Output

The output should contain the position. If the result is match the given M numbers, you will print the positions of them. Otherwise it wil be NULL.

Sample

InputOutput
3
4
4 6 7 9
3
3 3 3
4
4 6 3 8
2
1 2 3
NULL


Problem Setter: Redwan Ahmed

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