Make Them Equal

你有一个长度为 $n$ 的字符串 $s$（下标从 $1$ 开始）和一个字符 $c$。你可以执行若干次操作，在每次操作中你可以选择一个数 $x(1\leqslant x\leqslant n)$，然后将 $s$ 中所有下标不能被 $x$ 整除的位置上面的字符替换成 $c$。求使得最终得到的字符串 $s$ 中仅包含字符 $c$ 的最小操作次数，并给出每次操作中你选择的 $x$。 数据范围与约束： - $t$ 组数据，$1\leqslant t\leqslant 10^4$。 - $3\leqslant n\leqslant 3\times 10^5$。 - 字符串 $s$ 和字符 $c$ 仅由小写字母组成。 - $\sum n\leqslant 3\times 10^5$。 Translated by Eason_AC

Theofanis has a string $ s_1 s_2 \dots s_n $ and a character $ c $ . He wants to make all characters of the string equal to $ c $ using the minimum number of operations. In one operation he can choose a number $ x $ ( $ 1 \le x \le n $ ) and for every position $ i $ , where $ i $ is not divisible by $ x $ , replace $ s_i $ with $ c $ . Find the minimum number of operations required to make all the characters equal to $ c $ and the $ x $ -s that he should use in his operations.

The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of test cases. The first line of each test case contains the integer $ n $ ( $ 3 \le n \le 3 \cdot 10^5 $ ) and a lowercase Latin letter $ c $ — the length of the string $ s $ and the character the resulting string should consist of. The second line of each test case contains a string $ s $ of lowercase Latin letters — the initial string. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 3 \cdot 10^5 $ .

For each test case, firstly print one integer $ m $ — the minimum number of operations required to make all the characters equal to $ c $ . Next, print $ m $ integers $ x_1, x_2, \dots, x_m $ ( $ 1 \le x_j \le n $ ) — the $ x $ -s that should be used in the order they are given. It can be proved that under given constraints, an answer always exists. If there are multiple answers, print any.

3
4 a
aaaa
4 a
baaa
4 b
bzyx

0
1
2
2 
2 3

Let's describe what happens in the third test case: 1. $ x_1 = 2 $ : we choose all positions that are not divisible by $ 2 $ and replace them, i. e. bzyx $ \rightarrow $ bzbx; 2. $ x_2 = 3 $ : we choose all positions that are not divisible by $ 3 $ and replace them, i. e. bzbx $ \rightarrow $ bbbb.