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:
from collections import defaultdict as dfdict
def main():
	N,K,P=raw_input().split()
	n=int(N)
	k=int(K)
	p=int(P)
	s=raw_input().split()
	o=[int(x) for x in s]
	l=sorted(o)
	d=dfdict(list)
	j=0		
	for i in range(n-1):
		d[l[i]].append(0+j)
		if l[i+1]==l[i]:
			continue
		if l[i+1]-l[i]>k:
			j+=1
	d[l[n-1]].append(j)
	for __ in range(p):
		A,B=raw_input().split()
		a=int(A);b=int(B)
		if a==b:
			print "Yes"
		else:	
			if d[o[a-1]][0]==d[o[b-1]][0]:
					print "Yes" 
			else:
					print "No" 
main()