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.

#### Constraints

##### Subtask 1 [15%]

##### Subtask 2 [85%]

No additional constraints.

#### Input Specification

The first line contains two space-separated integers, and .

#### Output Specification

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

`6 4`

#### 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

`2 1`

#### Sample Output 2

`-1`

## Comments