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ZOJ Problem Set - 1487
Playing Cards

Time Limit: 2 Seconds      Memory Limit: 65536 KB

Gali comes to like playing cards recently. Here is an example of his favorite game: at the beginning, he holds a pile of 13 cards in his hand with the face values being 7, A, Q, 2, 8, 3, J, 4, 9, 5, K, 6, 10 from the top to the bottom. Then he takes the top card and placed it under the bottom card. Next he takes the current top card and puts it on the table. Gali will repeat these two steps until there is no more card in his hand. By then Gali will find that the face values of the cards, according to the order they have been placed on the table, form an increasing sequence: A, 2, 3, 4, 5, 6, 7, 8, 9, 10, J, Q, K.

Now let us assume that Gali has n cards in his hand, with each card numbered from 1 to n. If he does his first step -- taking the top card and placing it under the bottom card -- m times before doing the second step -- putting the current top card on to the table, he wants to determine the initial order of the cards in his hand so that after the game the sequence of the face values of the cards on the table will be in ascending order.

Input

The input contains several test cases. Each test case consists of two positive integers n and m where 1 <= n, m <= 2000.

Output

For each test case, output the initial sequence of the n cards in a line. Separate two numbers with a single space.

Sample Input

13 1

Sample Output

7 1 12 2 8 3 11 4 9 5 13 6 10

Author: CHEN, Gaoli
Source: ZOJ Monthly, February 2003
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