You are given a sequence of **n** integers **a**_{1} , a_{2} , ... , a_{n} 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 **a**_{i} , ... , a_{j}.

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.

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