A13141 | Interesting Subarray

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).