Problem Statement

Determine whether there is a sequence of $N integers X = (X_1, X_2, \ldots ,X_N)$ that satisfies all of the following conditions, and construct one such sequence if it exists.

• $0 \leq X_i \leq M$ for every $1 \leq i \leq N$.
• $L_i \leq X_{A_i} + X_{B_i} \leq R_i$ for every $1 \leq i \leq Q$.

Input

The input is given from Standard Input in the following format:
N M Q
A_1 B_1 L_1 R_1
A_2 B_2 L_2 R_2
$\vdots$
A_Q B_Q L_Q R_Q

Output

If there is an integer sequence that satisfies all of the conditions in the Problem Statement, print the elements $X_1, X_2, \ldots, X_N$ of one such sequence, separated by spaces. Otherwise, print -1.

Constraints

• $1 \leq N \leq 10000$
• $1 \leq M \leq 100$
• $1 \leq Q \leq 10000$
• $1 \leq A_i, B_i \leq N$
• $0 \leq L_i \leq R_i \leq 2 \times M$
• All values in the input are integers.

Sample Input 1

4 5 3
1 3 5 7
1 4 1 2
2 2 3 8

Sample Output 1

2 4 3 0

For X = (2,4,3,0), we have X_1 + X_3 = 5, X_1 + X_4 = 2, and X_2 + X_2 = 8, so all conditions are satisfied. There are other sequences, such as X = (0,2,5,2) and X = (1,3,4,1), that satisfy all conditions, and those will also be accepted.

Sample Input 2

3 7 3
1 2 3 4
3 1 9 12
2 3 2 4

Sample Output 2

-1

No sequence X satisfies all conditions.

见题面 Input 部分

见题面 Output 部分