Problem Description

There were $ N $ participants in the qualification round of CODE FESTIVAL 2016. Each participant is either a domestic student, a foreign student, or neither.

Only domestic or foreign students can qualify for the next round. They qualify in the order from the highest-ranked participant, following these conditions: Participants who are not students cannot qualify.

• A domestic student qualifies if the number of participants who have already qualified is less than $ A+B $.
• A foreign student qualifies if the number of participants who have already qualified is less than $ A+B $ and if their rank among foreign students is within the top $ B $.

You are given a string $ S $ representing the information about the participants. The $ i $-th character of $ S $ is a if the $ i $-th participant is a domestic student, b if the $ i $-th participant is a foreign student, and c if the $ i $-th participant is neither.

Create a program that outputs Yes if the participant at the $ i $-th position qualifies, and No otherwise, for all participants in order from the highest rank.

Input Format

The input is given from the standard input in the following format:

$ N $ $ A $ $ B $ $ S $

Output Format

Output $ N $ lines. The $ i $-th line should contain Yes if the $ i $-th participant qualifies, and No otherwise.

Sample Input and Output

Sample Input #1

10 2 3
abccabaabb

Sample Output #1

Yes
Yes
No
No
Yes
Yes
Yes
No
No
No

Sample Input #2

12 5 2
cabbabaacaba

Sample Output #2

No
Yes
Yes
Yes
Yes
No
Yes
Yes
No
Yes
No
No

Sample Input #3

5 2 2
ccccc

Sample Output #3

No
No
No
No
No

Notes/Hints

Constraints

• $1 \leq N, A, B \leq 100000$
• $A + B \leq N$
• The length of $ S $ is $ N $.
• $ S $ consists only of the characters a, b, and c.

Sample Explanation 1

Participants at positions $ 1, 2, 5, 6, 7 $ qualify.

Sample Explanation 2

The participant at position $ 6 $ is the third among foreign students and does not qualify.

见题面 Input 部分

见题面 Output 部分