Unique Gold Coin Distribution

You are given two integers: T representing the total number of gold coins and P representing the number of pirates. Your task is to find all possible ways to distribute the coins among the pirates subject to the following rules:

• Each pirate must receive at least one coin.
• All pirates receive a unique number of coins, i.e. no two pirates get the same number.
• The sum of coins received by all pirates must equal T.

In mathematical terms, if the coin counts are \(a_1, a_2, \dots, a_P\) with \(a_1 < a_2 < \dots < a_P\), then they must satisfy:

\(a_1 + a_2 + \dots + a_P = T\) and \(a_i \ge 1\) for all i.

If there is no valid distribution, output a single line with [].

inputFormat

The input consists of a single line containing two space-separated integers T and P where:

• T (1 ≤ T ≤ 10⁹) is the total number of gold coins.
• P (0 ≤ P ≤ 20) is the number of pirates.

Note: If P is 0, there is no valid distribution.

outputFormat

If a valid distribution exists, output each valid distribution on a separate line. For a distribution, print the coin amounts allocated to each pirate in increasing order separated by a single space. If more than one valid distribution exists, you may output them in any order.

If there is no valid distribution, output a single line containing [].

## sample

10 4

1 2 3 4

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