Given N and K, output the permutation of numbers from 1 to N such that the inversion count of the resultant sequence is K and it is lexicographically smallest possible.

Inversion count: For an array A, number of ordered pairs (i, j) such that A_i > A_j and i < j.

If no permutation with inversion count K is possible, output -1.

Input:

Single line containing N and K separated by a space.

Output:

Required permutation if it exist, else -1.

Constraints:​​​​​​​

• 1 ≤ N ≤ 3*10⁶
• 0 ≤ K ≤ 10¹⁴