You are given \(N\) strings and \(Q\) questions. Each question contains two values \(X\) and \(Y\). Print "Yes" if the \(X^{th}\) string is a subsequence of \(Y^{th}\) string or Yth string is a subsequence of Xth string, otherwise,print "No".

A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements. Read more about subsequences here.

Input format

First line: Two space-separated integers \(N\) and \(Q\)
Next N lines: \(N\) strings
Next Q lines: Two space-separated integers \(X\) and \(Y\)

Output format

Print the answer to each question in a new line.

Constraints

\(1 \le |S_i| \le 10^6\)

\(1 \le N \le 10^5\)

\(N \le\sum_{i=1}^{n}|S_i|\le 10^6 \)

\(1 \le Q \le 10^5\)

\(1 \le X,Y \le N\)

\(|Si|\) denotes length of ith string

Each string contains only lowercase alphabets.