Night has fallen, and alpacas have gathered around a campfire. They sit in a circle, that is, alpaca is to the right of alpaca , alpaca is to the right of alpaca , alpaca is to the right of alpaca , and so on. Each alpaca is waiting to be assigned a happiness index, . The alpaca is happy if the sum of its happiness index and the happiness index of the alpaca to its right is even. Otherwise, it is sad. Being a diligent herdsman, you decide to assign each of the alpacas a happiness index such that there are exactly happy alpacas.
Subtask 1 [15%]
Subtask 2 [85%]
No additional constraints.
The first line contains two space-separated integers, and .
If no solution exists, output . Otherwise, output space-separated integers, the happiness index for the alpaca . If there are multiple solutions, output any.
Note: Output must end with a newline with no trailing whitespace.
Sample Input 1
Sample Output 1
7 27 196 50 3 17
Explanation for Sample Output 1
The happy alpacas in this arrangement are alpaca , alpaca , alpaca , and alpaca . Note that this is not the only solution.
Sample Input 2
Sample Output 2