Problem B
Card Trick

The magician shuffles a small pack of cards, holds it face down and performs the following procedure:
-
The top card is moved to the bottom of the pack. The new top card is dealt face up onto the table. It is the Ace of Spades.
-
Two cards are moved one at a time from the top to the bottom. The next card is dealt face up onto the table. It is the Two of Spades.
-
Three cards are moved one at a time . . .
-
This goes on until the
th and last card turns out to be the of Spades.
This impressive trick works if the magician knows how to arrange the cards beforehand (and knows how to give a false shuffle). Your program has to determine the initial order of the cards for a given number of cards.
Input
On the first line of the input is a single positive integer
Output
For each test case, output a line with the correct
permutation of the values
Sample Input 1 | Sample Output 1 |
---|---|
2 4 5 |
2 1 4 3 3 1 4 5 2 |