Nobody knows, but N frogs live in Chef's garden.
Now they are siting on the X-axis and want to speak to each other. One frog can send a message to another one if the distance between them is less or equal to K.
Chef knows all P pairs of frogs, which want to send messages. Help him to define can they or not!
Note : More than 1 frog can be on the same point on the X-axis.

Input

The first line contains three integers N, K and P.
The second line contains N space-separated integers A1, A2, ..., AN denoting the x-coordinates of frogs".
Each of the next P lines contains two integers A and B denoting the numbers of frogs according to the input.

Output

For each pair print "Yes" without a brackets if frogs can speak and "No" if they cannot.

Constraints

1 ≤ N, P ≤ 10^5
0 ≤ Ai, K ≤ 10^9
1 ≤ A, B ≤ N

Example
Input:
5 3 3
0 3 8 5 12
1 2
1 3
2 5

Output:
Yes
Yes
No

Explanation
For pair (1, 2) frog 1 can directly speak to the frog 2 as the distance between them is 3 - 0 = 3 <= K .
For pair (1, 3) frog 1 can send a message to frog 2, frog 2 can send it to frog 4 and it can send it to frog 3.
For pair (2, 5) frogs can't send a message under current constraints.

见题面

见题面