Score : 800 points

Problem Statement

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.

Sample Input 1

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

Sample Output 1

4
2

In the first query, you can have at most 3 points in a good set. There exist two good sets: \{1,4,7\} and \{1,4,8\}. Therefore, the size of the union of all good sets is |\{1,4,7,8\}|=4.

In the second query, you can have at most 1 point in a good set. There exist two good sets: \{1\} and \{2\}. Therefore, the size of the union of all good sets is |\{1,2\}|=2.

Sample Input 2

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

Sample Output 2

4
6
11
2
3