Problem E
Dice Cup
![\includegraphics[width=0.7\textwidth ]{BluePlatonicDice.png}](/problems/dicecup/file/statement/en/img-0001.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 |