Grant, a sorter at SORT company, is interested in two things given two integers $n$ and $t$:

1. How many permutations of the numbers $1,2,\dots,n$ have exactly $t$ inversions?
2. What is the lexicographically smallest permutation among those with exactly $t$ inversions?

A permutation $A=(A_1,A_2,\dots,A_n)$ is considered lexicographically smaller than $B=(B_1,B_2,\dots,B_n)$ if there exists an index $1\le i\le n$ such that $A_1=B_1,\; A_2=B_2,\; \dots,\; A_{i-1}=B_{i-1}$ and $A_i<B_i$.

It is guaranteed that $0 \le t \le \frac{n(n-1)}{2}$.

inputFormat

The input consists of a single line containing two integers $n$ and $t$, separated by a space.

outputFormat

Output two lines:

• The first line contains a single integer representing the total number of permutations of $1,2,\dots,n$ with exactly $t$ inversions.
• The second line contains the lexicographically smallest permutation (as $n$ space-separated integers) among those with exactly $t$ inversions.

sample

3 0

1
1 2 3