Border Cells of a Grid

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem Statement

Count distinct border cells of an n-by-m grid; a cell is on the border if it lies in the first/last row or first/last column. All cells are border cells if n=1 or m=1.

Input

Two positive integers n m.

Output

Number of border cells as a 64-bit integer.

Subtasks

• Subtask 1 (20%): 1 ≤ n,m ≤ 20.

• Subtask 2 (30%): 1 ≤ n,m ≤ 1000.

• Subtask 3 (50%): 1 ≤ n,m ≤ 10^6.

Examples

Example 1

Input:

3 4

Output:

10

Explanation: Twelve total cells minus two interior cells give ten border cells.

Example 2

Input:

1 5

Output:

5

Explanation: All five cells of a one-row grid are border cells.