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

inputFormat

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

outputFormat

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

样例

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

4
2

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