405732: GYM102056 G Omnipotent … Garland

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 $$$A=\{A_0, A_1, \dots, A_{c - 1}\}~(A_i < A_{i + 1}, i = 0, 1, \dots, c - 2)$$$, 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:

• $$$0 \le x, y < \lvert S_i \rvert$$$
• $$$x \neq y$$$
• $$$x \equiv (y + 1) \pmod{\lvert S_i \rvert}$$$
• $$$t[{S_i}_x] = t[{S_i}_y] =$$$ "B"

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