Frequent values - 2

 You are given a sequence of n integers a1 , a2, ... , an in non-decreasing order. In addition to that, you are given several queries consisting of indices i and j (1 ≤ i ≤ j ≤ n). For each query, determine the most frequent value among the integers ai , ... , aj.

   Input

   Consists of several test cases. Each test case starts with a line containing two integers n and q (1 ≤ n, q ≤ 500000). The next line contains n integers a1 , ... , an (-500000 ≤ ai ≤ 500000, for each i ∈ {1, ..., n}) separated by spaces. You can assume that for each i ∈ {1, ..., n - 1}: ai ≤ ai+1. The following q lines contain one query each, consisting of two integers i and j (1 ≤ i ≤ j ≤ n), which indicate the boundary indices for the query.

   The last test case is followed by a line containing a single 0.

   Output

   For each query, print one line with one integer: The number of occurrences of the most frequent value within the given range.

10 3
-1 -1 1 1 1 1 3 10 10 10
2 3
1 10
5 10
0

1
4
3