A country has n cities. These n cities are connected using n - 1 bidirectional roads, such that it is possible to go from any city to any other city using these roads. City m is considered to be the capital of the country. The president of the country has asked your help in q queries.
In each query, you will be given two cities u and v. You need to find whether the shortest path from city u to city v passes through the capital of the city.
See sample case for better understanding
Input format:
First line contains two integers n and m, denoting the number of cities and the capital city.
Next n - 1 lines contains two integers u and v, denoting that there is a road between city u and city v.
Next line contains an integer q, denoting the number of queries.
Next q lines contain two integers u and v, describing the query.
Output format:
For each query, print "YES"(without quotes) if the shortest path from city u to city v passes through the capital, else print "NO"(without quotes). .
Constraints:
1 <= n, q <= 100000(1e5)
1 <= u, v, m <= n
In first query, shortest path between city 5 and 4 is: 5 -> 3 -> 4, which doesnot pass through capital city 2. Hence, answer is "NO".
In second query, shortest path is: 1 -> 2 -> 3 -> 4, which passes through capital. Hence, answer is "YES".
In third query, shortest path is 1 -> 2, which passes through capital and so answer is "YES".
In fourth query, shortest path is 2 -> 3, which passes through capital ans so answer is "YES".