Given a sequence $A_1, A_2, \ldots, A_N$ of length $N$. Write a program to process the following queries:

• s e: Output the number of pairs $(i, j)$ such that $s \le i < j \le e$ and $A_i > A_j$. ($1 \le s \le e \le N$)

Input

The first line contains the length of the sequence $N$ ($1 \le N \le 100{,}000$) and the number of queries $M$ ($1 \le M \le 100{,}000$).

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

The next $M$ lines each contain a query.

Output

For each query, output its answer on a separate line.

Examples

Example Input 1

5 3
1 4 2 3 1
1 2
3 5
1 5

Example Output 1

0
2
5