Dice Cup

\includegraphics[width=0.7\textwidth ]{BluePlatonicDice.png}

In many table-top games it is common to use different dice to simulate random events. A “d” or “D” is used to indicate a die with a specific number of faces, d4 indicating a four-sided die, for example. If several dice of the same type are to be rolled, this is indicated by a leading number specifying the number of dice. Hence, 2d6 means the player should roll two six-sided dice and sum the result face values.

Task

Write a program to compute the most likely outcomes for the sum of two dice rolls. Assume each die has numbered faces starting at 1 and that each face has equal roll probability.

Input

The input consists of a single line with two integer numbers, $N, M$, specifying the number of faces of the two dice.

Constraints

$4 \leq N,M\leq 20$ Number of faces.

Output

A line with the most likely outcome for the sum; in case of several outcomes with the same probability, they must be listed from lowest to highest value in separate lines.

Sample Input 1 Sample Output 1
6 6
7
Sample Input 2 Sample Output 2
6 4
5
6
7
Sample Input 3 Sample Output 3
12 20
13
14
15
16
17
18
19
20
21