Pebble#10837

Pebble

1 second
256 megabytes
Hard

This summer, Antun and Branka discovered an unusual beach, entirely covered with plastic pebbles washed ashore from containers that had fallen off cargo ships. They decided to take of these pebbles with them: some red and some blue.

In autumn, while reminiscing about the warm days, Antun and Branka invented a game with these pebbles. At the beginning, they arrange all pebbles in a row. Then the players take turns: on each move, a player must remove one pebble from either end of the row. The player who first collects red pebbles loses the game. Antun always makes the first move, and he wonders: can he guarantee victory regardless of Branka's moves? Your task is to help him answer this question.

Input

The first line contains two integers and k~(1 \le k < n \le 350).

The second line contains a sequence of characters or , where denotes a red pebble and denotes a blue pebble. It is guaranteed that the character appears at least 2 \cdot k - 1 times.

Output

Print "DA" if Antun can win regardless of Branka's moves, and "NE" otherwise.

Examples

Example 1

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Example 2

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Example 3

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