Informatics in MAC
Contest: Codeforces Round 932 (Div. 2)
Difficulty rating: 1200
Tags: constructive algorithms

In the Master's Assistance Center, Nyam-Nyam was given a homework assignment in informatics.

There is an array $$$a$$$ of length $$$n$$$, and you want to divide it into $$$k > 1$$$ subsegments$$$^{\dagger}$$$ in such a way that the $$$\operatorname{MEX} ^{\ddagger}$$$ on each subsegment is equal to the same integer.

Help Nyam-Nyam find any suitable division, or determine that it does not exist.

$$$^{\dagger}$$$A division of an array into $$$k$$$ subsegments is defined as $$$k$$$ pairs of integers $$$(l_1, r_1), (l_2, r_2), \ldots, (l_k, r_k)$$$ such that $$$l_i \le r_i$$$ and for each $$$1 \le j \le k - 1$$$, $$$l_{j + 1} = r_j + 1$$$, and also $$$l_1 = 1$$$ and $$$r_k = n$$$. These pairs represent the subsegments themselves.

$$$^{\ddagger}\operatorname{MEX}$$$ of an array is the smallest non-negative integer that does not belong to the array.

For example:

- $$$\operatorname{MEX}$$$ of the array $$$[2, 2, 1]$$$ is $$$0$$$, because $$$0$$$ does not belong to the array.
- $$$\operatorname{MEX}$$$ of the array $$$[3, 1, 0, 1]$$$ is $$$2$$$, because $$$0$$$ and $$$1$$$ belong to the array, but $$$2$$$ does not.
- $$$\operatorname{MEX}$$$ of the array $$$[0, 3, 1, 2]$$$ is $$$4$$$, because $$$0$$$, $$$1$$$, $$$2$$$, and $$$3$$$ belong to the array, but $$$4$$$ does not.

Input format:
Each test consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 10^5$$$) — the length of the array $$$a$$$.

The second line of each test case contains $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$ ($$$0 \le a_i < n$$$) — the elements of the array $$$a$$$.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$.

Output format:
For each test case, output a single integer $$$-1$$$ if a suitable division does not exist.

Otherwise, on the first line, output an integer $$$k$$$ ($$$2 \le k \le n$$$) — the number of subsegments in the division.

Then output $$$k$$$ lines — the division into subsegments. The $$$i$$$-th line should contain two integers $$$l_i$$$ and $$$r_i$$$ ($$$1 \le l_i \le r_i \le n$$$) — the boundaries of the $$$i$$$-th subsegment.

The following conditions must be satisfied:

- For all $$$1 \le j \le k - 1$$$, $$$l_{j + 1} = r_j + 1$$$;
- $$$l_1 = 1$$$, $$$r_k = n$$$.

If there are multiple possible solutions, output any of them.

Constraints:
Time limit: 1.0 s
Memory limit: 256.0 MB

Note:
In the first test case, the array $$$a$$$ can be divided into $$$2$$$ subsegments with boundaries $$$[1, 1]$$$ and $$$[2, 2]$$$:

- $$$\operatorname{MEX}$$$ of the first subsegment $$$[0]$$$ is $$$1$$$, as $$$0$$$ belongs to the subsegment, but $$$1$$$ does not.
- $$$\operatorname{MEX}$$$ of the second subsegment $$$[0]$$$ is $$$1$$$, as $$$0$$$ belongs to the subsegment, but $$$1$$$ does not.

In the second test case, it can be proven that the required division does not exist.

In the third test case, the array $$$a$$$ can be divided into $$$3$$$ subsegments with boundaries $$$[1, 3]$$$, $$$[4, 5]$$$, $$$[6, 8]$$$:

- $$$\operatorname{MEX}$$$ of the first subsegment $$$[0, 1, 7]$$$ is $$$2$$$, as $$$0$$$ and $$$1$$$ belong to the subsegment, but $$$2$$$ does not.
- $$$\operatorname{MEX}$$$ of the second subsegment $$$[1, 0]$$$ is $$$2$$$, as $$$0$$$ and $$$1$$$ belong to the subsegment, but $$$2$$$ does not.
- $$$\operatorname{MEX}$$$ of the third subsegment $$$[1, 0, 3]$$$ is $$$2$$$, as $$$0$$$ and $$$1$$$ belong to the subsegment, but $$$2$$$ does not.

Example input:
5
2
0 0
5
0 1 2 3 4
8
0 1 7 1 0 1 0 3
3
2 2 2
4
0 1 2 0

Example output:
2
1 1
2 2
-1
3
1 3
4 5
6 8
3
1 1
2 2
3 3
-1

Editorial: