P12566 [UOI 2023] An Array and Several More Arrays

There are $k$ arrays of integers $a_1, a_2, \ldots, a_k$, where the array with index $i$ contains $l_i$ elements. Let $n = l_1 + l_2 + \ldots + l_k$. You need to find $k$ integers $d_1, d_2, \ldots, d_k$ such that the numbers $(a_{i,j} + d_i)$ are pairwise distinct and satisfy $1 \leq a_{i,j} + d_i \leq n$.

The first line contains two integers $n$ and $k$ ($1 \le n \le 10^4$, $1 \le k \le 5$) -- the total number of elements in the arrays and the number of arrays, respectively. The next $k$ lines contain the arrays. The $i$-th line contains an integer $l_i$ ($1\le l_i\le n$) and $l_i$ integers $a_{i,1},a_{i,2},\ldots,a_{i,l_i}$ ($1 \le a_{i,j} \le n$) -- the length and elements of the $i$-th array, respectively. It is guaranteed that $n = l_1 + l_2 + \ldots + l_k$.

If the required values of $d$ do not exist, output a single line ``No``. Otherwise, output ``Yes`` on the first line. On the second line, output $k$ integers $d_1,d_2,\ldots,d_k$ -- the values that need to be added to the elements of the arrays to form a total of $n$ distinct integers from $1$ to $n$. If there are multiple correct answers, any one of them may be output.

In the first example, $d = [0,0,0,0,0]$ satisfies the condition, since after adding the corresponding values, the arrays $[1]$, $[2]$, $[3]$, $[4]$, $[5]$ are formed. In the second example, $d = [1,-5,1,1]$ satisfies the condition, since after adding the corresponding values, the arrays $[3,4]$, $[1]$, $[5]$, $[2,6]$ are formed. In the third example, $d = [0,1]$ satisfies the condition, since after adding the corresponding values, the arrays $[1,4,5,6]$ and $[2,3,7]$ are formed. ### Scoring - ($8$ points): $k=1$; - ($9$ points): $a_{i,j}+1=a_{i,j+1}$ for $1 \le i \le k$, $1 \le j < l_i$; - ($15$ points): $k \le 2$; - ($21$ points): $k \le 3$; - ($10$ points): $a_{i,j}+2=a_{i,j+1}$ for $1 \le i \le k$, $1 \le j < l_i$; - ($10$ points): $(\max_{j \in [1;l_i]} a_{i,j}) - (\min_{j \in [1;l_i]} a_{i,j})=(n-k)$ for $1 \le i \le k$; - ($10$ points): $n \le 30$; - ($17$ points): without additional constraints.