J. Gerrymandering
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Ignacio is conspiring to make their candidate win in the next election. He proposed a new method for electing the candidate, and it was accepted by the majority; this was the first step in his conspiracy. Now, you, as an "impartial" observer, have to help him in his next step of the conspiracy! (Or don't help him and see the consequences)

The method is the following: Every voter will sit at a circular table, and then you will divide the voters into $$$K$$$ groups. The members of each of the groups must sit adjacent to each other. After this, each of the groups decides by majority for which candidate they are going to vote; if there is not a majority inside the group, then that group doesn't vote for either candidate. The election would be decided by the candidate that gets the votes from more than half of the groups; if neither candidate achieves this, then another person would choose the partition (and you will see the consequences).

You know the favorite candidate for each of the voters; we have only two candidates (Jota and Leo), and Ignacio wants Jota to win. You have to make the $$$K$$$ groups so that Jota wins the election.

In other words: Given a circular array with two characters ('$$$\texttt{J}$$$' and '$$$\texttt{L}$$$'), you have to partition the array into $$$K$$$ subarrays so that the number of subarrays in which there are more $$$\texttt{J}$$$'s than $$$\texttt{L}$$$'s is greater than $$$\frac{K}{2}$$$.

Input

The first line contains $$$N\; \left(1\le N\le 2\times 10^5\right)$$$ and $$$K$$$ $$$(1\le K \le N$$$) — the number of voters and the number of groups, respectively.

The second line contains $$$N$$$ characters $$$c_1, c_2, \dots, c_n\;$$$ ($$$c_i$$$ is '$$$\texttt{J}$$$' or '$$$\texttt{L}$$$') — the circular array representing the favorite candidate of the $$$i$$$-th voter.

Output

If you can divide the array so that Jota wins, then print 'YES' and in the next line print $$$K$$$ numbers $$$a_1, a_2,\dots, a_k$$$ ($$$1\le a_1 \lt a_2 \lt \cdots \lt a_k\le N$$$) representing the partition of the circular array. The members of the $$$i$$$-th ($$$1\le i \lt k$$$) group would be $$$\{a_i,a_i+1,a_i+2,\dots, a_{i+1}-1\}$$$, and the members of the last group would be $$$\{a_k, a_k+1, \dots,N,1,2,\dots, a_1-1\}$$$.

Otherwise, if you can't divide the array so that Jota wins, print 'NO'.

Examples
Input
5 3
J L J J L
Output
YES
1 4 5
Input
5 3
J L J L L
Output
NO