Sherlock and Inversions

Watson gives to Sherlock an array of N integers denoted by A1, A2 ... AN.
Now he gives him Q queries of form Li, Ri. For each such query Sherlock has to report the number of inversions in subarray denoted by [Li, Ri].

Inversions in a subarray denoted by [a, b] are number of pairs (i, j) such that ai < jb and Ai > Aj.

Input

First line contains N and Q. Next line contains N space separated integers denoting array A.
Each of the next Q lines contain two space separated integers denoting Li, Ri.

Output

For each query, print the required answer in one line.

Limits

Subtask 1 (20%): 1 ≤ N, Q ≤ 103

Subtask 2 (20%): 1 ≤ N ≤ 103 and 1 ≤ Q ≤ 105

Subtask 3 (60%): 1 ≤ N, Q ≤ 105

Subtask 4 (0%): Sample

Sample Input 1

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

Sample Output 1

0
2
5

Explanation

query1: Number of inversions in B = [1, 4] is 0.

query2: Number of inversions in B = [2, 3, 1] is 2 since B[0]>B[2] and B[1]>B[2].

query3: Number of inversions in original array is 5.