ACL Contest 1 - Keep Distances

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

Difficulty: UNKNOWN_DIFFICULTY

Starter code:

Solutions:
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)


import sys
readline = sys.stdin.readline
INF = 10 ** 18 + 3
(N, K) = map(int, input().split())
X = list(map(int, readline().split())) + [INF]
left = [None] * N
r = 0
for i in range(N):
	while r < N and X[r + 1] - X[i] < K:
		r += 1
	left[i] = (r, i)
left = [left]
nb = N.bit_length()
for _ in range(nb):
	res = [None] * N
	for idx in range(N):
		(r, i) = left[-1][idx]
		if r >= N - 1:
			res[idx] = (N, None)
		else:
			(r1, i1) = left[-1][r + 1]
			if r1 == N:
				res[idx] = (N, None)
			else:
				res[idx] = (r1, i + i1)
	left.append(res)
right = [None] * N
l = N - 1
for i in range(N - 1, -1, -1):
	while 0 < l and X[i] - X[l - 1] < K:
		l -= 1
	right[i] = (l, i)
right = [right]
for _ in range(nb):
	res = [None] * N
	for idx in range(N):
		(l, i) = right[-1][idx]
		if l <= 0:
			res[idx] = (-1, None)
		else:
			(l1, i1) = right[-1][l - 1]
			if l1 == -1:
				res[idx] = (-1, None)
			else:
				res[idx] = (l1, i + i1)
	right.append(res)
Q = int(readline())
Ans = [None] * Q
for qu in range(Q):
	(l, r) = map(int, readline().split())
	l -= 1
	vn = l
	li = 0
	ml = 0
	for j in range(nb - 1, -1, -1):
		(vf, ix) = left[j][vn]
		if vf < r:
			vn = vf + 1
			li += ix
			ml += 1 << j
		if vn >= r:
			break
	if vn < r:
		ml += 1
		li += vn
	l -= 1
	r -= 1
	vn = r
	ri = 0
	mr = 0
	for j in range(nb - 1, -1, -1):
		(vf, ix) = right[j][vn]
		if l < vf:
			vn = vf - 1
			ri += ix
			mr += 1 << j
		if vn <= l:
			break
	if l < vn:
		mr += 1
		ri += vn
	Ans[qu] = ri - li + ml
print('\n'.join(map(str, Ans)))