Sunset

• Time limit: 1.00 s
• Memory limit: 512 MB

There are $n$ skyscrapers in a row. The sun illuminates some of the skyscrapers from the left: a skyscraper is in the sun if it is higher than any skyscraper to the left.

Your task is to process $q$ queries where each query has some range $[a,b]$. If we assume that only the skyscrapers in the range $[a,b]$ exist, how many of them are in the sun?

Input

The first input line has two integers $n$ and $q$: the number of skyscrapers and queries. The skyscrapers are numbered $1,2,\dots,n$.

The second line has $n$ integers $h_1, h_2, \dots, h_n$: the heights of the skyscrapers.

Finally, there are $q$ lines, each having two integers $a$ and $b$ ($1 \le a \le b \le n$): the range of the query is $[a,b]$.

Output

For each query, print one integer: the number of skyscrapers in the sun.

Example

Input:
5 3
4 1 2 2 3
1 5
2 5
3 4

Output:
1
3
1

Subtask 1 (16 points)

• $1 \leq n, q \leq 2000$
  
• $1 \leq h_{i} \leq 10^9$
  

Subtask 2 (35 points)

• $1 \leq n \leq 10^5$
  
• $1 \leq q \leq 2 \cdot 10^5$
  
• $1 \leq h_{i} \leq 100$
  

Subtask 3 (49 points)

• $1 \leq n \leq 10^5$
  
• $1 \leq q \leq 2 \cdot 10^5$
  
• $1 \leq h_{i} \leq 10^9$