Problem:
Score : 300 points

Problem Statement

There is a grid with infinitely many rows and columns. In this grid, there is a rectangular region with consecutive N rows and M columns, and a card is placed in each square in this region.
The front and back sides of these cards can be distinguished, and initially every card faces up.

We will perform the following operation once for each square contains a card:

For each of the following nine squares, flip the card in it if it exists: the target square itself and the eight squares that shares a corner or a side with the target square.

It can be proved that, whether each card faces up or down after all the operations does not depend on the order the operations are performed.
Find the number of cards that face down after all the operations.

Constraints

1 \leq N,M \leq 10^9

All input values are integers.

Input

Input is given from Standard Input in the following format:

N M

Output

Print the number of cards that face down after all the operations.

Sample Input 1

2 2

Sample Output 1

0

We will flip every card in any of the four operations. Thus, after all the operations, all cards face up.

Sample Input 2

1 7

Sample Output 2

5

After all the operations, all cards except at both ends face down.

Sample Input 3

314 1592

Sample Output 3

496080

Solution in JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

// E: LISDL
"use strict";

// no more time (17 mins left); pseudocode for brute force:
// 1. loop through range 1..N while saving current min and max
// 2. every time min and max changes, increase maxA and maxB
// 3. if maxA reaches the input A and maxB for B, it is possible
// ^wrong (10 minutes left)

// pseudocode for optimised implementation:
// 1. check if A is less than or equal to N/2 and B is less than or equal
// to (N-A)/2
// this is because if a subsequence with length N
// has A increasing items (e.g. - A = 3, N = 5, 1 0 3 -1 5)
// the max for B is the number of digits in the middle of A?
// no more time
// for construction, write A increasing digits first
// then write B decreasing digits between each digit in A:
// e.g. - [] are increasing, () are decreasing
// A = 2, B = 3, B = 5
// [1] [0] [3] [-1] [5]

const DEBUG_MODE = false;
const rawInput = DEBUG_MODE
  ? "30000 30000 30000"
  : require("fs")
    .readFileSync("/dev/stdin", "utf8")
    .trim();

const process = inputRaw => {
  const inputs = inputRaw.split(" ");
  const N = inputs[0];
  const A = inputs[1];
  const B = inputs[2];

  console.log(A+B <= N ? -1 : "");
};

process(rawInput);