Fixed that and tried a bit more. The only way I can try to debug this is to see 
what causes a TLE error and what causes a RE error. If an assertion fails then 
it's a RE error. It seems to be responding with -1 when I output the 18 numbers 
on a line for the windmill blade counts. I don't know what it wants.

local function inv(a, b)
        local m, c, d = b, 1, 0
        while b ~= 1 do
                a, b, c, d = b%a, a, d - c*math.floor(b/a), c
        end
        return d%m
end
 
function remainder(m, b)
        local M = 1
        for i = 1, #m do M = M*m[i] end
        local x, Mi = 0
        for i = 1, #m do
                Mi = M/m[i]
                x = x + b[i]*inv(Mi, m[i])*Mi
        end
        return x%M
end

local function getresponse(input)
        print(input.."\n")
        io.flush()
        return io.read()
end

local T = tonumber(io.read():match("%d+"))
for _ = 1, T do
        local n = {7, 11, 13, 15, 16, 17}
        local a = {}
        for i = 1, #n do
                local result = getresponse((n[i].." "):rep(18):sub(1, -2))
                local count, values = 0, 0
                for v in result:gmatch("%d+") do
                        count = count + v
                        values = values + 1
                end
                assert(values == 18)
                a[i] = count%n[i]
        end
        local gophers = remainder(n, a)
        local verdict = getresponse(gophers)
        assert(verdict == "1")
end

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