- 84

## Statement

## Goal

Terry loves candies.He just got a new batch of candies and he's wondering about how he should eat them.

Terry is trying to eat those

`N`candies and he can put up to

`K`candies in his mouth at once.

What are the possibilities for Terry to eat his candies ?

For example, let's say Terry wants to eat 3 candies and that he can put in his mouth up to 2 candies :

He can just eat 1 candy three times in a row.

He can eat 1 candy, and then 2.

Or, he can also eat 2, and then eat 1.

The output should then be :

1 1 1

1 2

2 1

Input

**Two integers separated by a space**:

`N`the number of candies,

`K`the size of Terry's mouth.

Output

The possibilities need to be sorted using the lexicographical order.

**For each possibility**:**A line of integers separated by spaces**: The possibility, i.e. the numbers of candy that Terry puts in his mouth at each step.Constraints

`N`≤

`K`≤

Example

Input

1 1

Output

1

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