Problem Statement

We have a grid with N rows and M columns. The square (i,j) at the i-th row from the top and j-th column from the left has an integer $(i-1) \times M + j$ written on it.
Let us perform the following operation on this grid.

• For every square (i,j) such that i+j is odd, replace the integer on that square with 0.

Answer Q questions on the grid after the operation.
The i-th question is as follows:

• Find the sum of the integers written on all squares (p,q) that satisfy all of the following conditions, modulo 998244353.
• $A_i \le p \le B_i$.
• $C_i \le q \le D_i$.

Input

The input is given from Standard Input in the following format:
N M
Q
A_1 B_1 C_1 D_1
A_2 B_2 C_2 D_2
$\vdots$
A_Q B_Q C_Q D_Q

Output

Print Q lines.
The i-th line should contain the answer to the i-th question as an integer.

Constraints

• All values in the input are integers.
• $1 \le N,M \le 10^9$
• $1 \le Q \le 2 \times 10^5$
• $1 \le A_i \le B_i \le N$
• $1 \le C_i \le D_i \le M$

Sample Input 1

5 4
6
1 3 2 4
1 5 1 1
5 5 1 4
4 4 2 2
5 5 4 4
1 5 1 4

Sample Output 1

28
27
36
14
0
104

The grid in this input is shown below.

This input contains six questions.

• The answer to the first question is 0+3+0+6+0+8+0+11+0=28.
• The answer to the second question is 1+0+9+0+17=27.
• The answer to the third question is 17+0+19+0=36.
• The answer to the fourth question is 14.
• The answer to the fifth question is 0.
• The answer to the sixth question is 104.

Sample Input 2

1000000000 1000000000
3
1000000000 1000000000 1000000000 1000000000
165997482 306594988 719483261 992306147
1 1000000000 1 1000000000

Sample Output 2

716070898
240994972
536839100

For the first question, note that although the integer written on the square (10^9,10^9) is 10^{18}, you are to find it modulo 998244353.

Sample Input 3

999999999 999999999
3
999999999 999999999 999999999 999999999
216499784 840031647 84657913 415448790
1 999999999 1 999999999

Sample Output 3

712559605
648737448
540261130

见题面 Input 部分

见题面 Output 部分