Clarke and puzzle

Accepts: 129
Submissions: 322
Time Limit: 4000/2000 MS (Java/Others)
Memory Limit: 65536/65536 K (Java/Others)
Problem Description
Clarke is a patient with multiple personality disorder. One day, Clarke split into two personality $a$ and $b$, they are playing a game. There is a $n*m$ matrix, each grid of this matrix has a number $c_{i, j}$. $a$ wants to beat $b$ every time, so $a$ ask you for a help. There are $q$ operations, each of them is belonging to one of the following two types: 1. They play the game on a $(x_1, y_1)-(x_2, y_2)$ sub matrix. They take turns operating. On any turn, the player can choose a grid which has a positive integer from the sub matrix and decrease it by a positive integer which less than or equal this grid's number. The player who can't operate is loser. $a$ always operate first, he wants to know if he can win this game. 2. Change $c_{i, j}$ to $b$.
Input
The first line contains a integer $T(1 \le T \le 5)$, the number of test cases. For each test case: The first line contains three integers $n, m, q(1 \le n, m \le 500, 1 \le q \le 2*10^5)$ Then $n*m$ matrix follow, the $i$ row $j$ column is a integer $c_{i, j}(0 \le c_{i, j} \le 10^9)$ Then $q$ lines follow, the first number is $opt$. if $opt=1$, then $4$ integers $x_1, y_1, x_1, y_2(1 \le x_1 \le x_2 \le n, 1 \le y_1 \le y_2 \le m)$ follow, represent operation $1$. if $opt=2$, then $3$ integers $i, j, b$ follow, represent operation $2$.
Output
For each testcase, for each operation $1$, print $Yes$ if $a$ can win this game, otherwise print $No$.
Sample Input
1
1 2 3
1 2
1 1 1 1 2
2 1 2 1
1 1 1 1 2
Sample Output
Yes
No

Hint:
The first enquiry: $a$ can decrease grid $(1, 2)$'s number by $1$. No matter what $b$ operate next, there is always one grid with number $1$ remaining . So, $a$ wins.
The second enquiry: No matter what $a$ operate, there is always one grid with number $1$ remaining. So, $b$ wins.