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

Inversions in a subarray denoted by [a, b] are number of pairs (i, j) such that a ≤ i < j ≤ b and A_i > A_j.

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 L_i, R_i.

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

Constraints
20% files: 1 ≤ N, Q ≤ 10³
20% files: 1 ≤ N ≤ 10³ and 1 ≤ Q ≤ 10⁵
60% files: 1 ≤ N, Q ≤ 10⁵
1 ≤ A_i ≤ 10⁹
1 ≤ L_i ≤ R_i ≤ N