In a two-player competitive match, for any positive integer , we define the Best of format as follows: the two players continue to compete until one of them wins times, thereby winning the overall match. The Best of format includes a maximum of games and a minimum of games.

For any two positive integers and , we define the Best of of Best of format as follows: the two players compete in a major match using the Best of format, which consists of a maximum of major games and a minimum of major games. Each major game is a Best of format, consisting of a maximum of minor games and a minimum of minor games. For example, Team A and Team B play a Best of of Best of match. Here are some possible outcomes (we use to represent a win for Team A and to represent a win for Team B):

• 000111000 (Team A loses the first and third major games 0:3, wins the second major game 3:0, so the overall score is a 1:2 loss for Team A);
• 0110000110 (Team A loses the first and second major games 2:3, so the overall score is a 0:2 loss for Team A).
  

Team A and Team B are currently engaged in a DotA2 match using the Best of of Best of format. To the spectators, this is an exciting event! However, unknown to the spectators, the entire match outcome is predetermined: there is a "script" of length represented by a binary string , where the results of the minor games will continuously repeat this pattern of . Having this information, you want to know the match results when the "script" string is repeated from each position (see the sample explanation for details).

输入描述:

The first line of input contains three integers , ,  , whose meanings are already given in the statement.

The second line of input contains a binary "script" string  with length .

输出描述:

Output a binary string  of length , where   represents the final match result when repeating the script string  starting from the -th position of .

3 1 1
001

001

7 2 2
1010101

1110111

10 5 3
1001011001

0011010011

10 2 4
1010000011

0000011110

2 100000 100000
01

01

备注:

For the second sample test, the situation starting from each position is as follows:

Starting from the first position, the match results in , and the final match sequence is . Team A wins 2:1 in major matches, with scores of 2:1, 1:2, 2:0, respectively.

Starting from the second position, the match results in , and the final match sequence is . Team A wins 2:1 in major matches, with scores of 1:2, 2:1, 2:1, respectively.

Starting from the third position, the match results in , and the final match sequence is . Team A wins 2:0 in major matches, with scores of 2:1, 2:1, respectively.

Starting from the fourth position, the match results in , and the final match sequence is . Team A loses 1:2 in major matches, with scores of 1:2, 2:0, 1:2, respectively.

Starting from the fifth position, the match results in , and the final match sequence is . Team A wins 2:0 in major matches, with scores of 2:1, 2:1, respectively.

Starting from the sixth position, the match results in , and the final match sequence is . Team A wins 2:1 in major matches, with scores of 2:1, 1:2, 2:1, respectively.

Starting from the seventh position, the match results in , and the final match sequence is . Team A wins 2:1 in major matches, with scores of 2:0, 1:2, 2:1, respectively.