Problem: There are N points on a number line, i-th of which is placed on coordinate X_i. These points are numbered in the increasing order of coordinates. In other words, for all i (1 \leq i \leq N-1), X_i < X_{i+1} holds. In addition to that, an integer K is given.

Process Q queries.

In the i-th query, two integers L_i and R_i are given. Here, a set s of points is said to be a good set if it satisfies all of the following conditions. Note that the definition of good sets varies over queries.

* Each point in s is one of X_{L_i},X_{L_i+1},\ldots,X_{R_i}.
* For any two distinct points in s, the distance between them is greater than or equal to K.
* The size of s is maximum among all sets that satisfy the aforementioned conditions.



For each query, find the size of the union of all good sets.

Constraints

* 1 \leq N \leq 2 \times 10^5
* 1 \leq K \leq 10^9
* 0 \leq X_1 < X_2 < \cdots < X_N \leq 10^9
* 1 \leq Q \leq 2 \times 10^5
* 1 \leq L_i \leq R_i \leq N
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N K
X_1 X_2 \cdots X_N
Q
L_1 R_1
L_2 R_2
\vdots
L_Q R_Q


Output

For each query, print the size of the union of all good sets in a line.

Examples

Input

5 3
1 2 4 7 8
2
1 5
1 2


Output

4
2


Input

15 220492538
4452279 12864090 23146757 31318558 133073771 141315707 263239555 350278176 401243954 418305779 450172439 560311491 625900495 626194585 891960194
5
6 14
1 8
1 13
7 12
4 12


Output

4
6
11
2
3

Solution (in PYTHON3):

Solution:
import sys
readline = sys.stdin.buffer.readline

n,k = map(int,readline().split())
vs = list(map(int,readline().split()))

L=18
xid=[0]*(n*L)
xsum=[0]*(n*L)
yid=[0]*(n*L)
ysum=[0]*(n*L)

j=n
for i in reversed(range(n)):
	while i<j and vs[i]+k<=vs[j-1]:
		j-=1
	xid[i*L+0]=j
	xsum[i*L+0]=j
	for lv in range(1,L):
		a=xid[i*L+lv-1]
		if a==n:
			xid[i*L+lv]=n
		else:
			xid[i*L+lv]=xid[a*L+lv-1]
			xsum[i*L+lv]=xsum[i*L+lv-1]+xsum[a*L+lv-1]

j=-1
for i in range(n):
	while j<i and vs[j+1]+k<=vs[i]:
		j+=1
	yid[i*L+0]=j
	ysum[i*L+0]=j
	for lv in range(1,L):
		a=yid[i*L+lv-1]
		if a==-1:
			yid[i*L+lv]=-1
		else:
			yid[i*L+lv]=yid[a*L+lv-1]
			ysum[i*L+lv]=ysum[i*L+lv-1]+ysum[a*L+lv-1]

q=int(readline())
for tmp in range(q):
	l,r=map(int,readline().split())
	l-=1
	r-=1
	ans=0
	
	i=l
	ans-=i
	for lv in reversed(range(L)):
		if xid[i*L+lv]<=r:
			ans-=xsum[i*L+lv]
			i=xid[i*L+lv]
	
	i=r
	ans+=i+1
	for lv in reversed(range(L)):
		if yid[i*L+lv]>=l:
			ans+=ysum[i*L+lv]+(1<<lv)
			i=yid[i*L+lv]
	
	print(ans)