B. Interesting Subarray
constructive algorithms; greedy; math
For an array \(a\) of integers let's denote its maximal element as \(\max(a)\), and minimal as \(\min(a)\). We will call an array \(a\) of \(k\) integers interesting if \(\max(a) - \min(a) \ge k\). For example, array \([1, 3, 4, 3]\) isn't interesting as \(\max(a) - \min(a) = 4 - 1 = 3 < 4\) while array \([7, 3, 0, 4, 3]\) is as \(\max(a) - \min(a) = 7 - 0 = 7 \ge 5\).You are given an array \(a\) of \(n\) integers. Find some interesting nonempty subarray of \(a\), or tell that it doesn't exist.An array \(b\) is a subarray of an array \(a\) if \(b\) can be obtained from \(a\) by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end. In particular, an array is a subarray of itself.
The first line contains integer number \(t\) (\(1 \le t \le 10\,000\)). Then \(t\) test cases follow.The first line of each test case contains a single integer \(n\) (\(2\le n \le 2\cdot 10^5\)) — the length of the array.The second line of each test case contains \(n\) integers \(a_1, a_2, \dots, a_n\) (\(0\le a_i \le 10^9\)) — the elements of the array.It is guaranteed that the sum of \(n\) over all test cases does not exceed \(2 \cdot 10^5\).
For each test case, output ""NO"" in a separate line if there is no interesting nonempty subarray in \(a\). Otherwise, output ""YES"" in a separate line. In the next line, output two integers \(l\) and \(r\) (\(1\le l \le r \le n\)) — bounds of the chosen subarray. If there are multiple answers, print any.You can print each letter in any case (upper or lower).
In the second test case of the example, one of the interesting subarrays is \(a = [2, 0, 1, 9]\): \(\max(a) - \min(a) = 9 - 0 = 9 \ge 4\).