Yutori

Takahashi has decided to work on K days of his choice from the N days starting with tomorrow.

You are given an integer C and a string S. Takahashi will choose his workdays as follows:

• After working for a day, he will refrain from working on the subsequent C days.
• If the i-th character of S is x, he will not work on Day i, where Day 1 is tomorrow, Day 2 is the day after tomorrow, and so on.

Find all days on which Takahashi is bound to work.

Constraints

• 1 \leq N \leq 2 \times 10^5
• 1 \leq K \leq N
• 0 \leq C \leq N
• The length of S is N.
• Each character of S is o or x.
• Takahashi can choose his workdays so that the conditions in Problem Statement are satisfied.

Input

Input is given from Standard Input in the following format:

N K C S

Output

Print all days on which Takahashi is bound to work in ascending order, one per line.

Examples

Input

11 3 2 ooxxxoxxxoo

Output

6

Input

5 2 3 ooxoo

Output

1 5

Input

5 1 0 ooooo

Output

Input

16 4 3 ooxxoxoxxxoxoxxo

Output

11 16

inputFormat

Input

Input is given from Standard Input in the following format:

N K C S

outputFormat

Output

Print all days on which Takahashi is bound to work in ascending order, one per line.

Examples

Input

11 3 2 ooxxxoxxxoo

Output

6

Input

5 2 3 ooxoo

Output

1 5

Input

5 1 0 ooooo

Output

Input

16 4 3 ooxxoxoxxxoxoxxo

Output

11 16

样例

5 2 3
ooxoo

1
5

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