CF1935B.Informatics in MAC

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.

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 $10^5$ .

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.

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.