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).