Given a sequence $A_1, A_2, \ldots, A_N$ of length $N$ and an integer $K$. Write a program to execute the following query:

• l r: output the number of pairs $(i, j)$ satisfying $l \le i < j \le r$ and $\mathrm{abs}(A_i - A_j) \le K$.

Input

The first line contains two integers $N$ $(1 \le N \le 100{,}000)$ and $K$ $(1 \le K \le 100{,}000)$, representing the length of the sequence and the parameter $K$.

The second line contains $N$ integers $A_1, A_2, \ldots, A_N$ $(1 \le A_i \le 100{,}000)$.

The third line contains an integer $M$ $(1 \le M \le 100{,}000)$, representing the number of queries.

The next $M$ lines each contain two integers $l, r$ $(1 \le l \le r \le N)$, representing a query.

Output

For each query, output a line containing a single integer representing the answer.

Examples

Input 1

4 31
1 16 32 64
4
1 4
1 2
2 4
2 3

Output 1

3
1
1
1