CodeForces 547E：Mike and Friends（AC自动机+DFS序+主席树）

Posted 2020-11-21 hua-dong

What-The-Fatherland is a strange country! All phone numbers there are strings consisting of lowercase English letters. What is double strange that a phone number can be associated with several bears!

In that country there is a rock band called CF consisting of n bears (including Mike) numbered from 1 to n.

Phone number of i-th member of CF is s_i. May 17th is a holiday named Phone Calls day. In the last Phone Calls day, everyone called all the numbers that are substrings of his/her number (one may call some number several times). In particular, everyone called himself (that was really strange country).

Denote as call(i, j) the number of times that i-th member of CF called the j-th member of CF.

The geek Mike has q questions that he wants to ask you. In each question he gives you numbers l, r and k and you should tell him the number

Input

The first line of input contains integers n and q (1 ≤ n ≤ 2 × 10⁵ and 1 ≤ q ≤ 5 × 10⁵).

The next n lines contain the phone numbers, i-th line contains a string s_iconsisting of lowercase English letters ().

The next q lines contain the information about the questions, each of them contains integers l, r and k (1 ≤ l ≤ r ≤ n and 1 ≤ k ≤ n).

Output

Print the answer for each question in a separate line.

Examples

Input

5 5
a
ab
abab
ababab
b
1 5 1
3 5 1
1 5 2
1 5 3
1 4 5

Output

7
5
6
3
6

题意：给定N个串，M次询问，每次询问[L,R]里含多少个X。

思路：（第一次做，结合主席树那里还是不太好想）。对N个串建立AC自动机，建立Fail树，然后得到DFS序。那么，对于每个串S，假设其长度为L，S在AC自动机上面跑，其每个前缀Si在AC自动机上面得到最大深度，对应的Fail树位置，贡献加1，保证这个贡献在Si的后缀的子树里（比如abcdef，那么跑到abcd时，在fail树上面对应的位置贡献加1 ，对于后缀abcd,bcd,cd,d的子树都含这个贡献）。 

        关键是如何出现子树来自于[L,R]的贡献。开始我以为以dfs序为X轴，以来自的串为Y轴建立主席树，查询的时候查询区间[in[u],out[u]]，即子树里关键字在[L,R]里的个数。但是发现没有转移关系。所以想不走了。

看了其他人的代码，是以每个串，以来自的串为X轴（从长的前缀到短的前缀），以dfs序为X轴，保证了前缀和的正确性，查询的时候查询区间[L-1,R]的区间在[in[[u],out[u]]的数量。