B. Range and Partition
binary search; constructive algorithms; data structures; greedy; two pointers
Given an array \(a\) of \(n\) integers, find a range of values \([x, y]\) (\(x \le y\)), and split \(a\) into exactly \(k\) (\(1 \le k \le n\)) subarrays in such a way that: Each subarray is formed by several continuous elements of \(a\), that is, it is equal to \(a_l, a_{l+1}, \ldots, a_r\) for some \(l\) and \(r\) (\(1 \leq l \leq r \leq n\)). Each element from \(a\) belongs to exactly one subarray. In each subarray the number of elements inside the range \([x, y]\) (inclusive) is strictly greater than the number of elements outside the range. An element with index \(i\) is inside the range \([x, y]\) if and only if \(x \le a_i \le y\). Print any solution that minimizes \(y - x\).
The input consists of multiple test cases. The first line contains a single integer \(t\) (\(1 \leq t \leq 3 \cdot 10^4\)) — the number of test cases. Description of the test cases follows.The first line of each test case contains two integers \(n\) and \(k\) (\(1 \le k \le n \le 2 \cdot 10^5\)) — the length of the array \(a\) and the number of subarrays required in the partition.The second line of each test case contains \(n\) integers \(a_1, a_2, \ldots, a_n\) (\(1 \le a_i \le n\)) where \(a_i\) is the \(i\)-th element of the array.It is guaranteed that the sum of \(n\) over all test cases does not exceed \(2\cdot10^5\).
For each test case, print \(k+1\) lines.In the first line, print \(x\) and \(y\) — the limits of the found range.Then print \(k\) lines, the \(i\)-th should contain \(l_i\) and \(r_i\) (\(1\leq l_i \leq r_i \leq n\)) — the limits of the \(i\)-th subarray.You can print the subarrays in any order.
In the first test, there should be only one subarray, which must be equal to the whole array. There are \(2\) elements inside the range \([1, 2]\) and \(0\) elements outside, if the chosen range is \([1, 1]\), there will be \(1\) element inside (\(a_1\)) and \(1\) element outside (\(a_2\)), and the answer will be invalid.In the second test, it is possible to choose the range \([2, 2]\), and split the array in subarrays \((1, 3)\) and \((4, 4)\), in subarray \((1, 3)\) there are \(2\) elements inside the range (\(a_2\) and \(a_3\)) and \(1\) element outside (\(a_1\)), in subarray \((4, 4)\) there is only \(1\) element (\(a_4\)), and it is inside the range.In the third test, it is possible to choose the range \([5, 5]\), and split the array in subarrays \((1, 4)\), \((5, 7)\) and \((8, 11)\), in the subarray \((1, 4)\) there are \(3\) elements inside the range and \(1\) element outside, in the subarray \((5, 7)\) there are \(2\) elements inside and \(1\) element outside and in the subarray \((8, 11)\) there are \(3\) elements inside and \(1\) element outside.