A balanced bracket sequence of length 2n is a string of n opening brackets ( and n closing brackets ) such that at every prefix the number of ( seen so far is at least the number of ) seen so far, and the two counts are equal at the very end. The nesting depth at any point is the current count of unmatched open brackets; the sequence's overall depth is the maximum depth reached at any prefix.
Given n and a maximum allowed depth d, count how many balanced bracket sequences of length 2n have depth never exceeding d at any point.
Input format
Line 1: two integers n and d.
Output format
A single integer: the count of balanced sequences of length 2n with depth always ≤ d.
Constraints
- 1 ≤ n ≤ 12
- 1 ≤ d ≤ n