Problem Description

You have an image (matrix) with $n$ rows and $m$ columns, and the image has $n\times m$ pixels.

Initially, all pixels are black, and the RGB value is $(0,0,0)$. Each operation can change one number in the RGB of a pixel.

After each operation, please output whether the image is left-right symmetric.

Left-right symmetry: that is, for any $i,j$, it always holds that the RGB value of the pixel in row $i$, column $j$ is equal to the RGB value of the pixel in row $i$, column $m-j+1$.

Input Format

The first line contains three integers $n,m,q$, where $q$ is the number of operations.

The next $q$ lines each contain four integers $i,j,t,c$, meaning to increase the $t$-th number of the RGB value of the cell in row $i$, column $j$ by $c$. If any number in any RGB value exceeds $255$, it is automatically taken modulo $256$.

Output Format

After each operation, if the image is left-right symmetric, output Yes; otherwise output No. Outputs of each query are separated by newlines.

6 6 9
1 2 3 4
5 6 3 4
1 5 3 4
5 1 3 4
1 3 2 260
1 4 2 4
2 2 3 5
2 5 3 7
2 2 3 258

No
No
No
Yes
No
Yes
No
No
Yes

Hint

This problem uses bundled Subtask tests.

For Subtask 2, it is guaranteed that each variable is generated uniformly at random.

For $100\%$ of the data, $1\le n,m\le 100$, $1\le q\le 500$, $1\le i\le n$, $1\le j\le m$, $t\in \{1,2,3\}$, $1\le c\le 10^9$.

Translated by ChatGPT 5