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.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)))