Given two integers $N$ and $K$. Your task is to construct an array $A$ such that:

• $A$ is a permutation with size $N$. (i.e. All $N$ integers from $1$ to $N$ must appear exactly once in $A$)
• The number of inversions inside $A$ is exactly $K$.

A pair of elements $(A_i, A_j)$ is considered an inversion if and only if $i \lt j$ and $A_i \gt A_j$.

For example, in the array $A=[2, 4, 1, 3]$, there are three pairs of inversion: $(A_1, A_3)$, $(A_2, A_3)$ and $(A_2, A_4)$.

Please note that there might be no valid solution.

Input

The only line contains two integers $N$ and $K$.

Output

If there is no valid solution, output $-1$.

Otherwise, output $N$ integers on a single line, denoting the array $A$. If there are multiple answers, output any of them.

Subtasks

For all test cases, $2 \le N \le 2 \times 10^5$, $0 \le K \le 10^{18}$