Rikka finally fell asleep on the top of the lunar tower. She dreamed about LCR's unique garland which she had always treated with great interest. The garland is made of $$$n$$$ flowers of two types: Bauhinia Blakeana and Cerasus Yedoensis. For convenience, we use abbreviations to call them "B" and "C". The $$$n$$$ flowers form a ring, that is, each flower has an integer index in $$$[0, n)$$$ such that the flowers $$$i$$$ and $$$((i + 1) \bmod n)$$$ are adjacent.
Rikka has chosen two magic positive integers $$$m,k$$$. Now she wants to divide the garland into $$$m$$$ shorter ones such that the length of each sub-garland is a multiple of $$$k$$$, flowers in each sub-garland keep in order as they used to be in the garland, and there exist two distinct "B"s in each sub-garland that are adjacent. You need to answer if there exist valid partitions, and if so, output any of them.
Formally, let $$$t[i]~(i = 0, 1, \dots, n - 1)$$$ be the type of the flower with index $$$i$$$ (either "B" or "C"). A sub-garland containing $$$c$$$ flowers can be described as an ascending sequence $$$A=\{A_0, A_1, \dots, A_{c - 1}\}~(A_i \lt A_{i + 1}, i = 0, 1, \dots, c - 2)$$$, which represents the indices in the original garland of those flowers. We also regard $$$A$$$ as the set of all items in the sequence $$$A$$$. Rikka wants to find $$$m$$$ sequences $$$S_1, S_2, \dots, S_m$$$ such that $$$\cup_{i = 1}^{m} {S_i} = \{0, 1, \dots , n-1\}$$$, $$$\sum_{i = 1}^{m} {\lvert S_i \rvert} = n$$$, and for $$$i = 1, 2, \dots, m$$$, $$$\lvert S_i \rvert$$$ is a multiple of $$$k$$$ and there exists $$$x, y~(x, y \in \mathbb{Z})$$$ meeting the conditions:
The first line contains an integer $$$T~(1\le T\le 10^5)$$$, the number of test cases. Then $$$T$$$ test cases follow.
The input format of each test case is as follows:
The first line contains three integers $$$n, m, k~(1\le n, m, k\le 10^6)$$$, the length of the garland, the number of sub-garlands and the factor of sub-garlands' lengths.
The second line contains a string $$$t$$$ of length $$$n$$$, where the $$$i$$$-th character is either "B" or "C", representing $$$t[i]~(i=0, 1, \dots, n-1)$$$, the type of the flower $$$i$$$.
It is guaranteed that the sum of $$$n$$$ in all test cases is at most $$$10^6$$$.
Answer each test case in order. For each test case, the output format is as follows:
The first line contains a string "Yes" or "No" (without the quotation marks). Output "Yes" if there exists a valid partition, or "No" otherwise.
If the answer is "Yes", output the sub-garlands in the following $$$m$$$ lines. In each line, the first integer is the length of that sub-garland $$$\lvert S_i \rvert$$$. The following $$$\lvert S_i \rvert$$$ integers are the indices in the original garland of the flowers in it, in ascending order.
4 6 2 2 BBCCBB 6 2 3 BBCCBB 4 4 1 BBBB 12 2 3 BBCCBCCBBCCC
Yes 2 0 1 4 2 3 4 5 Yes 3 0 1 2 3 3 4 5 No Yes 6 0 1 2 3 5 6 6 4 7 8 9 10 11
