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A. Diverse Permutation

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPermutation *p* is an ordered set of integers *p*_{1}, *p*_{2}, ..., *p*_{n}, consisting of *n* distinct positive integers not larger than *n*. We'll denote as *n* the length of permutation *p*_{1}, *p*_{2}, ..., *p*_{n}.

Your task is to find such permutation *p* of length *n*, that the group of numbers |*p*_{1} - *p*_{2}|, |*p*_{2} - *p*_{3}|, ..., |*p*_{n - 1} - *p*_{n}| has exactly *k* distinct elements.

Input

The single line of the input contains two space-separated positive integers *n*, *k* (1 ≤ *k* < *n* ≤ 10^{5}).

Output

Print *n* integers forming the permutation. If there are multiple answers, print any of them.

Examples

Input

3 2

Output

1 3 2

Input

3 1

Output

1 2 3

Input

5 2

Output

1 3 2 4 5

Note

By |*x*| we denote the absolute value of number *x*.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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