Copying the Solution for https://codeforces.com/problemset/problem/1713/C

BuildPermutation.kt

import kotlin.math.*

fun debugln(str: String) = println(str)
//fun debugln(@Suppress("UNUSED_PARAMETER") unused: String) = {}

fun search(n: Int) : List<Int> {
    val ans = (0 until n).toMutableList()

    fun fill(r: Int) {
        if (r < 0) {
            return
        }

        // The sqrt that should exist.
        val s = sqrt(2.0 * r).toInt().let { it * it }
        assert(r < s && s < 2 * r)
        // ??? Why is this range? 
        val l = s - r
        (l .. r).forEach { ans[it] = s - it }
        // Recurse down to the remaining range.
        fill(l - 1)
        debugln("$l to $r is filled with $s")
    }

    fill(n - 1)
    return ans
}

fun main() {
    repeat(readLine()!!.toInt()) {
        val len = readLine()!!.toInt()
        println(search(len).joinToString(separator=" "))
    }
}