Given n candies and k people. In the first turn, the first person gets 1 candy, the second gets 2 candies, and so on till k people. In the next turn, the first person gets k + 1 candies, the second person gets k + 2 candies and so on until all the sweets are distributed. If the number of candies is less than the required number of candies at every turn, then the person receives the remaining number of candies.

Find the total number of candies every person has at the end.

Input

The number of candies n (n ≤ 1018) and the number of people k (k ≤ 106).

Output

Print k integers: how many candies will get each person in total.