Some parenthesizations

Given a natural number $n$ , compute the number of correct parenthesizations with $n$ opening and $n$ closing parentheses, with just one restriction: the substring “)()” is not allowed.

For instance, for $n = 4$ there are four correct parenthesizations: “(((())))”, “(()(()))”, “(())(())” and “()((()))”.

Input

Input consists of several cases, each one with an $n$ between 1 and $10^4$ .

Output

For each $n$ , print the result modulo $10^9 + 7$ .

Problem information

Author: Xavier Povill

Generation: 2026-01-25T10:12:31.825Z