Problem Statement

You are given $a length-N sequence (A_1, A_2, \ldots, A_N)$ of positive integers, and Q queries about the sequence.
For each $q = 1, 2, \ldots, Q$, the q-th query gives you an integer pair (l_q, r_q);
print the number of integer triplets (i, j, k) such that

• $l_q \leq i \lt j \lt k \leq r_q$, and
• A_i = A_j = A_k.

Input

The input is given from Standard Input in the following format:
N Q
$A_1 A_2 \ldots A_N$
l_1 r_1
l_2 r_2
$\vdots$
l_Q r_Q

Output

Print Q lines.
For $q = 1, 2, \ldots, Q$, the q-th line should contain the answer to the q-th query.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq Q \leq 2 \times 10^5$
• $1 \leq A_i \leq 2 \times 10^5$
• $1 \leq l_q \leq r_q \leq N$
• All values in the input are integers.

Sample Input 1

10 4
2 7 1 8 2 8 1 8 2 8
1 10
1 9
2 10
5 5

Sample Output 1

5
2
4
0

For the first query, there are five triplets of integers that satisfy the conditions in the problem statement:
(1, 5, 9), (4, 6, 8), (4, 6, 10), (4, 8, 10), and (6, 8, 10).

Sample Input 2

20 10
2 2 2 2 1 1 2 2 1 1 1 2 1 2 1 2 2 1 2 1
12 16
17 18
12 18
4 9
13 13
2 5
6 13
2 14
7 14
8 12

Sample Output 2

1
0
5
2
0
1
11
55
8
1

见题面 Input 部分

见题面 Output 部分