A company has employees, who form a tree hierarchy where each employee has a boss, except for the general director.
Your task is to process queries of the form: who is employee 's boss levels higher up in the hierarchy?
The first line has two integers and : the number of employees and queries. The employees are numbered , and employee is the general director.
The next line has integers : for each employee their boss.
Finally, there are lines describing the queries. Each line has two integers and : who is employee 's boss levels higher up?
Print the answer for each query. If such a boss does not exist, print .