local fmt = require "fmt"

local function josephus(n, k, m)
    if k <= 0 or m <= 0 or n <= k or n <= m then
         error("one or more parameters are invalid")
    end
    local killed = {}
    local survived = {}
    for i = 1, n do survived[i] = i - 1 end
    local start = k
    while true do
        local finish = #survived
        local i = start
        local deleted = 0
        while i <= finish do
            killed:insert(survived:remove(i - deleted))
            if #survived == m then return {survived, killed} end
            ++deleted
            i += k
        end
        start = i - finish
    end
    return {survived, killed}
end

local triples = { {5, 2, 1}, {41, 3, 1}, {41, 3, 3} }
for triples as triple do
    local [n, k, m] = triple
    print($"Prisoners = {n}, Step = {k}, Survivors = {m}")
    local sk = josephus(n, k, m)
    print($"Survived   : {fmt.swrite(sk[1])}")
    print($"Kill order : {fmt.swrite(sk[2])}")
    print()
end