You are given a sequence of integers a_1, a_2, ..., a_n in non-decreasing order. In addition to that, you are given several queries consisting of indices and (1 \leq i \leq j \leq n). For each query, determine the most frequent value among the integers a_i, \ldots, a_j.
Consists of several test cases. Each test case starts with a line containing two integers and (1 \leq n, q \leq 500000). The next line contains integers a_1, \ldots, a_n (-500000 \leq a_i \leq 500000, for each i \in \{1, \ldots, n\}) separated by spaces. You can assume that for each i \in \{1, \ldots, n-1\}: a_i \leq a_{i+1}. The following lines contain one query each, consisting of two integers and (1 \leq i \leq j \leq n), which indicate the boundary indices for the query.
The last test case is followed by a line containing a single .
For each query, print one line with one integer: The number of occurrences of the most frequent value within the given range.
Пример 1