Dice Cup

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.

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.

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

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

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 |