Gorilla and Noobish_Monk found three numbers $n$, $m$, and $k$ ($m < k$). They decided to construct a permutation$^{\dagger}$ of length $n$.

For the permutation, Noobish_Monk came up with the following function: $g(i)$ is the sum of all the numbers in the permutation on a prefix of length $i$ that are not greater than $m$. Similarly, Gorilla came up with the function $f$, where $f(i)$ is the sum of all the numbers in the permutation on a prefix of length $i$ that are not less than $k$. A prefix of length $i$ is a subarray consisting of the first $i$ elements of the original array.

For example, if $n = 5$, $m = 2$, $k = 5$, and the permutation is $[5, 3, 4, 1, 2]$, then:

• $f(1) = 5$, because $5 \ge 5$; $g(1) = 0$, because $5 > 2$;
• $f(2) = 5$, because $3 < 5$; $g(2) = 0$, because $3 > 2$;
• $f(3) = 5$, because $4 < 5$; $g(3) = 0$, because $4 > 2$;
• $f(4) = 5$, because $1 < 5$; $g(4) = 1$, because $1 \le 2$;
• $f(5) = 5$, because $2 < 5$; $g(5) = 1 + 2 = 3$, because $2 \le 2$.

Help them find a permutation for which the value of $\left(\sum_{i=1}^n f(i) - \sum_{i=1}^n g(i)\right)$ is maximized.

$^{\dagger}$A permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in any order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation (as $2$ appears twice in the array) and $[1,3,4]$ is also not a permutation (as $n=3$, but $4$ appears in the array).