# 2458. Frequent values

You are given a sequence of $n$ integers $a_1, a_2, \ldots, a_n$ in non-decreasing order. In addition to that, you are given several queries consisting of indices $i$ and $j$ $(1 \le i \le j \le n)$. For each query, determine the most frequent value among the integers $a_i, \ldots, a_j$.

### 输入

The input consists of several test cases. Each test case starts with a line containing two integers $n$ and $q$ $(1 \leq n, q \leq 100000)$. The next line contains $n$ integers $a_1, \ldots, a_n$ $(-100~000 \leq a_i \leq 100~000, \forall i \in \{1, \ldots, n\})$ separated by spaces. You can assume that for each $i \in \{1, ..., n-1\}$: $a_i \leq a_{i+1}$. The following $q$ lines contain one query each, consisting of two integers $i$ and $j$ $(1 \leq i \leq j \leq n)$, which indicate the boundary indices for the query.

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

### 输出

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

### 样例

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

Output
1
4
3


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