#P1440. Moonfang'sBirthday

Moonfang'sBirthday

It's Moonfang'sbirthday,and his friends decided to buy him a copy of XianJianQiXiaZhuan V.

Since some offriends have more money available than others, nobody has to pay more than hecan afford. Every contribution will be a multiple of 1 cent,i.e.,nobody can payfractions of a cent.

Everybody writesdown the maxumum amount he is able to contribute. Taking into account thesemaximum amounts from everybody, your task is to share the cost of the presentas fairly as possible. That means, you minimize the largest distance of thecontributions to 1/n-th of the total cost. 

In case of atie, minimize the second largest distance, and so on. Since the smallest unitof contribution is 1 cent, there might be more than one possible division ofthe cost. In that case, persons with a higher maximum amount pay more. If thereis still ambiguity, those who come first in the list pay more.

Since you boughtthe present, it is your task to figure out how much everybody has to pay.

Input

On the first line a positive integer: the number of test cases, at most 200. After that per test case:
• One line with two integers p and n: the price of the present in cents (1 ≤ p ≤ 1 000 000) and the number of people (2 ≤ n ≤ 10000) who contribute to the present (including you).
• One line with n integers ai (1 ≤ ai ≤ 1 000 000), where ai is the maximum amount, in cents, that the i-th person on the list is able to contribute.

Output

Per test case:
• One line with n integers: the amounts each person has to contribute according to the scheme. If the total cost cannot be divided according to the above rules, the line must contain "IMPOSSIBLE" instead.

Sample Input

3 
20 4 
10 10 4 4 
7 3 
1 1 4 
34 5 
9 8 9 9 4

Sample Output

</p>
6 6 4 4 
IMPOSSIBLE 
8 7 8 7 4 

HINT

Source