You are given three integers n, pos, and k.

There are n people standing in a line, indexed from $0$ to n $- 1$. Each person independently chooses to face either left, denoted by 'L', or right, denoted by 'R'.

A person at index i is visible to the observer at index pos if:

• i $<$ pos and the person at i faces left ('L').

• i $>$ pos and the person at i faces right ('R').

The direction chosen by the person at index pos does not affect the count of visible people.

Return the total number of valid direction assignments for all n people such that exactly k people are visible to the observer at index pos.

Constraints:

• $1 \le$ n $\le 10^5$

• $0 \le$ pos, k $\le$ n $- 1$

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