# 描述

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 $$\sum_{i = l} ^ r call(i, k)$$

## Input

The first line of input contains integers $n$ and $q$ ($1 ≤ n ≤ 2 × 10^5$ and $1 ≤ q ≤ 5 × 10^5$).

The next $n$ lines contain the phone numbers, $i$-th line contains a string $s_i$ consisting of lowercase English letters ($1 ≤ \sum_\limits{i = 1} ^ n |s_i| ≤ 2 × 10^5$).

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.

Input Output

# 思路

• 先不考虑$[l, r]$的限制，即考虑字符串$s_k$在一个字符集合中的出现次数。
• 只需要对字符集合建立AC自动机，$val$维护前缀的出现次数。
• 因为fail树中$s_k$是其子节点的后缀，所以再加上子树节点的$val$值。
• 这样就把问题转化为了求子树节点的权值之和。
• 于是我们只需要以fail树的DFS序建线段树维护区间和即可。
• 接下来考虑$[l, r]$的限制。这个很简单，把线段树给可持久化一下就好了。
• 当然解决这个二维查询还有其它姿势，可以按结点深度离线用树状数组查询（口胡一下，实现也不难）。

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