CF1792D.Fixed Prefix Permutations

You are given $n$ permutations $a_1, a_2, \dots, a_n$ , each of length $m$ . Recall that a permutation of length $m$ is a sequence of $m$ distinct integers from $1$ to $m$ .

Let the beauty of a permutation $p_1, p_2, \dots, p_m$ be the largest $k$ such that $p_1 = 1, p_2 = 2, \dots, p_k = k$ . If $p_1 \neq 1$ , then the beauty is $0$ .

The product of two permutations $p \cdot q$ is a permutation $r$ such that $r_j = q_{p_j}$ .

For each $i$ from $1$ to $n$ , print the largest beauty of a permutation $a_i \cdot a_j$ over all $j$ from $1$ to $n$ (possibly, $i = j$ ).

The first line contains a single integer $t$ ( $1 \le t \le 10^4$ ) — the number of testcases.

The first line of each testcase contains two integers $n$ and $m$ ( $1 \le n \le 5 \cdot 10^4$ ; $1 \le m \le 10$ ) — the number of permutations and the length of each permutation.

The $i$ -th of the next $n$ lines contains a permutation $a_i$ — $m$ distinct integers from $1$ to $m$ .

The sum of $n$ doesn't exceed $5 \cdot 10^4$ over all testcases.

For each testcase, print $n$ integers. The $i$ -th value should be equal to the largest beauty of a permutation $a_i \cdot a_j$ over all $j$ ( $1 \le j \le n$ ).