Rick-Roll Virus

Interview

Time limit2sMemory limit1024 MB

Summary

Given a line of N people with infected ones marked R, decide whether M cures can stop the virus that spreads K cells per day.

Level: Medium4 of 10
Topics: Greedy, Intervals
Solved: No attempts yet

Problem

In 2033, while a vote to pick the top meme in Harunaland ends with Rick Astley as the winner, the Rick-Roll Virus spreads through Harunaland. Anyone infected hums Never gonna give you up without fail, so haru_202 wants to stop the virus.

$N$ people live in a straight line, each one next to the next. An infected person at $x=i$ passes the virus after 1 day to the people at $x = \max(1, i-K)$ , $\cdots$ , $i$ , $\cdots$ , $\min(N, i+K)$ .

After 1 day, can haru_202 cure every infected person with $M$ doses of the cure? Each person can receive only one dose.

Input

The first line contains integers $N$ , $M$ , and $K$ separated by spaces. $(1 \leq N \leq 10\,000;$ $0 < M \leq N;$ $0 \leq K \leq \lfloor\frac{N}{2}\rfloor)$

The second line contains a string $S$ of length $N$ that shows the infection status of each person. $S_i$ is the status of the person at $x=i$ as follows. $(1 \leq i \leq N)$

.: not infected
R: infected

Output

After 1 day, print Yes if haru_202 can cure every person infected by the Rick-Roll Virus with $M$ doses of the cure, otherwise print No.

Examples2

Example 1
Input
```
5 3 1
..R..
```
Expected output
```
Yes
```
Example 2
Input
```
10 1 1
RRRRRRRRRR
```
Expected output
```
No
```