Consecutive Subsequence Sums

Problem Description

Given the numbers $1$ to $n$, you need to find several consecutive numbers whose sum equals $m$. Clearly there can be many such schemes; output every one of them, following the format shown in the sample.

Input Format

The first line contains two integers $n$ and $m$.

Output Format

Several lines of output, each line a valid scheme given as a closed interval: $[a,b]$ means the consecutive integers from $a$ to $b$. When multiple schemes exist, output them in increasing order of $a$.

Sample Input

20 15

Sample Output

[1,5]
[4,6]
[7,8]
[15,15]

Hint

$1+2+3+4+5 = 15$

$4+5+6 = 15$

$7+8 = 15$

$15 = 15$

$n, m \le 100000000$.