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