Problem Description
a and
b, they are playing a game.
There is a
n∗m matrix, each grid of this matrix has a number
ci,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
(x1,y1)−(x2,y2) 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
ci,j to
b.
Input
T(1≤T≤5), the number of test cases.
For each test case:
The first line contains three integers
n,m,q(1≤n,m≤500,1≤q≤2∗105)
Then
n∗m matrix follow, the
i row
j column is a integer
ci,j(0≤ci,j≤109)
Then
q lines follow, the first number is
opt.
if
opt=1, then
4 integers
x1,y1,x1,y2(1≤x1≤x2≤n,1≤y1≤y2≤m) follow, represent operation
1.
if
opt=2, then
3 integers
i,j,b follow, represent operation
2.
Output
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.
nim取子游戏+前缀和