Your task is to create a permutation of numbers $1,2,\dots,n$ that has exactly $k$ inversions.

An inversion is a pair $(a,b)$ where $a<b$ and $p_a>p_b$ where $p_i$ denotes the number at position $i$ in the permutation.

Input

The only input line has two integers $n$ and $k$.

Output

Print a line that contains the permutation. You can print any valid solution.

Constraints

• $1 \le n \le 10^6$
• $0 \le k \le \frac{n(n-1)}{2}$

Example

Input:

5 4

Output:

1 5 2 4 3