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

def root(parent,n) :
    if parent[n] == n :
        return n
    parent[n] = root(parent,parent[n])
    return parent[n]

def connect(parent,a,b) :
    ar , br = root(parent,a) , root(parent,b)
    parent[ar] = br

n , p , d = map(int,sys.stdin.readline().split())
lists = map(int,sys.stdin.readline().split())
parent = [0]*(n+1)
best = []
for i,j in enumerate(lists) :
    best.append((j,i))
best.sort()
for i in range(n) :
    parent[i] = i

for i in range(n-1) :
    if best[i+1][0]-best[i][0] <= p:
        connect(parent,best[i+1][1],best[i][1])

for __ in range(d) :
    x , y = map(int,sys.stdin.readline().split())
    x , y = x-1 , y-1
    print "Yes" if root(parent,x)==root(parent,y) else "No"