An Array and Several More Arrays

There are $k$ arrays of integers $a_1,a_2,\dots ,a_k$, where the array with index $i$ contains $l_i$ elements. Let $n=l_1+l_2+\dots +l_k$.

You need to find $k$ integers $d_1,d_2,\dots ,d_k$ such that the numbers $(a_{i,j}+d_i)$ are pairwise distinct and satisfy $1\le a_{i,j}+d_i\le n$.

Input

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 $a_{i,1},a_{i,2},\dots ,a_{i,l_i}$ ($1\le a_{i,j}\le n$) – the length and elements of the $i$-th array, respectively.

It is guaranteed that $n=l_1+l_2+\dots +l_k$.

Output

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 $d_1,d_2,\dots ,d_k$ – 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.

Examples

Note

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

1. ($8$ points): $k=1$;

2. ($9$ points): $a_{i,j}+1=a_{i,j+1}$ for $1\le i\le k$, $1\le j<l_i$;

3. ($15$ points): $k\le 2$;

4. ($21$ points): $k\le 3$;

5. ($10$ points): $a_{i,j}+2=a_{i,j+1}$ for $1\le i\le k$, $1\le j<l_i$;

6. ($10$ points): $({\max }_{j\in [1;l_i]}{a}_{i,j})-({\min }_{j\in [1;l_i]}{a}_{i,j})=(n-k)$ for $1\le i\le k$;

7. ($10$ points): $n\le 30$;

8. ($17$ points): without additional constraints.