Document Combination and Similarity Query

Fusu has not slept for 36 hours while working on her theoretical computer science assignment. To catch some sleep, she discovered n documents. The i-th document is represented by a sequence \(a_i\). Fusu plans to combine these documents using two types of operations:

• 1 x y: Concatenate document \(a_x\) to the end of document \(a_y\), then delete document \(a_x\). It is guaranteed that after a 1 operation, the deleted document will not appear in any subsequent operation.
• 2 x y: Query whether documents \(a_x\) and \(a_y\) are similar.

Two documents \(a_x\) and \(a_y\) are defined as similar if it is possible to rearrange the elements of \(a_x\) in some order so that it becomes equal to \(a_y\). In other words, they are similar if they have the same multiset of elements.

Example:
Suppose \(a_1 = [1,2]\), \(a_2 = [3,4]\), \(a_3 = [1,2,3,4]\). After performing the operation 1 1 2, document \(a_1\) is appended to \(a_2\) (so \(a_2\) becomes \([3,4,1,2]\)) and \(a_1\) is deleted. Then, executing 2 2 3 will return YES since \(a_2\) can be rearranged as \([1,2,3,4]\), which is equal to \(a_3\).

inputFormat

The first line contains two integers \(n\) and \(q\) --- the number of documents and the number of operations.

Then, \(n\) lines follow. The i-th of these lines begins with an integer \(k_i\) (the length of the \(i\)-th document), followed by \(k_i\) integers representing the elements of \(a_i\). It is recommended to sort each sequence internally (or maintain a count) since similarity only depends on the multiset of elements.

After that, \(q\) lines follow, each describing an operation in one of the following two formats:

• 1 x y
• 2 x y

All indices are 1-indexed.

outputFormat

For each operation of the form 2 x y, output a single line containing YES if document \(a_x\) and \(a_y\) are similar, and NO otherwise.

sample

3 2
2 1 2
2 3 4
4 1 2 3 4
1 1 2
2 2 3

YES