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 a ≤ i < j ≤ b 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.
Constraints
20% files: 1 ≤ N, Q ≤ 103
20% files: 1 ≤ N ≤ 103 and 1 ≤ Q ≤ 105
60% files: 1 ≤ N, Q ≤ 105
1 ≤ Ai ≤ 109
1 ≤ Li ≤ Ri ≤ N
query1: Number of inversions in B = [1, 4] is 0.
query2: Number of inversions in B = [2, 3, 1] are 2 since B[0]>B[2] and B[1]>B[2].
query3: Number of inversions in original array are 5.
