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.
n,k,p=map(int,raw_input().split())

arr=list(map(int,raw_input().split()))
a=[]
for i in range(n):
	a+=[(arr[i],i+1)]
a.sort()
arr[a[0][1]-1]=0
j=0
for t in xrange(1,n):
	if (a[t][0]-a[t-1][0])>k:
		j+=1
	q=a[t][1]
	arr[q-1]=j

while p>0:
	x,y=map(int,raw_input().split())
	x-=1
	y-=1	
	if arr[x]==arr[y]:
		print "Yes"
	else: 
		print "No"
		
	p-=1