Problem: 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.

Solution (in PYTHON):

Solution:
import sys
from operator import itemgetter

n,k,p = map(int,sys.stdin.readline().split())

l = list(map(int,sys.stdin.readline().split()))

l1 = sorted(enumerate(l,1),key=itemgetter(1))

d = {}

path = 0

item,prev_dist = l1[0]
d[item] = 0

for item,dist in l1[1:]:
    if dist-prev_dist > k:
        path += 1
    d[item] = path
    prev_dist = dist

for i in xrange(p):
    x1,x2 = map(int,sys.stdin.readline().split())
    if d[x1]==d[x2]:
        print "Yes"
    else:
        print "No"