Shallow sequences#4440
Denis wrote a program that removes all characters from a string except for "(" and ")". Now he is interested in the number of different correct bracket sequences of length that can be obtained.
It is known that, due to his beliefs, Denis runs his program only on valid mathematical expressions in which the maximum nesting depth of brackets is exactly .
The only line of input contains two integers (1 \leq n \leq 50) and (1 \leq k \leq n).
Output a single integer — the required number of sequences modulo 10^9+7.
Example 1