Ex - Constrained Sums

AtCoder

IDabc277_h

Time4000ms

Memory256MB

Difficulty—

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 $1 \leq i \leq Q$. ## 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. ## Input The input is given from Standard Input in the following format: $N$ $M$ $Q$ $A_1$ $B_1$ $L_1$ $R_1$ $A_2$ $B_2$ $L_2$ $R_2$ $\vdots$ $A_Q$ $B_Q$ $L_Q$ $R_Q$ [samples]

Samples

Input #1

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.

Input #2

Output #2

\-1

No sequence $X$ satisfies all conditions.

API Response (JSON)

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