A11181 | Merge Sort

Merge sort is a well-known sorting algorithm. The main function that sorts the elements of array $a$ with indices from $[l,r)$ can be implemented as follows:

1. If the segment $[l,r)$ is already sorted in non-descending order (that is, for any $i$ such that $l<=i<r-1$ $a[i]<=a[i+1]$ ), then end the function call;
2. Let ;
3. Call $mergesort(a,l,mid)$ ;
4. Call $mergesort(a,mid,r)$ ;
5. Merge segments $[l,mid)$ and $[mid,r)$ , making the segment $[l,r)$ sorted in non-descending order. The merge algorithm doesn't call any other functions.

The array in this problem is $0$ -indexed, so to sort the whole array, you need to call $mergesort(a,0,n)$ .

The number of calls of function $mergesort$ is very important, so Ivan has decided to calculate it while sorting the array. For example, if $a={1,2,3,4}$ , then there will be $1$ call of $mergesort$ — $mergesort(0,4)$ , which will check that the array is sorted and then end. If $a={2,1,3}$ , then the number of calls is $3$ : first of all, you call $mergesort(0,3)$ , which then sets $mid=1$ and calls $mergesort(0,1)$ and $mergesort(1,3)$ , which do not perform any recursive calls because segments $(0,1)$ and $(1,3)$ are sorted.

Ivan has implemented the program that counts the number of $mergesort$ calls, but now he needs to test it. To do this, he needs to find an array $a$ such that $a$ is a permutation of size $n$ (that is, the number of elements in $a$ is $n$ , and every integer number from $[1,n]$ can be found in this array), and the number of $mergesort$ calls when sorting the array is exactly $k$ .

Help Ivan to find an array he wants!

The first line contains two numbers $n$ and $k$ ( $1<=n<=100000$ , $1<=k<=200000$ ) — the size of a desired permutation and the number of $mergesort$ calls required to sort it.

If a permutation of size $n$ such that there will be exactly $k$ calls of $mergesort$ while sorting it doesn't exist, output $-1$ . Otherwise output $n$ integer numbers $a[0],a[1],...,a[n-1]$ — the elements of a permutation that would meet the required conditions. If there are multiple answers, print any of them.