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.
Consists of several test cases. Each test case starts with a line containing two integers n and q (1≤n,q≤105). The next line contains n integers a1,a2,...,an (−105≤ai≤105). 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.
For each query, print one line with one integer: the number of occurrences of the most frequent value within the given range.