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 The input consists of several test cases. Each test case starts with a line containing two integers n and q (1 ≤ n, q ≤ 100000). The next line contains n integers a1, . . . , an (−100000 ≤ ai ≤ 100000, 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. Note: A naive algorithm may not run in time! Sample Input 10 3 -1 -1 1 1 1 1 3 10 10 10 23 1 10 5 10 0 Sample Output 1 4 3