local mce, mfl, msq, mmi, mma, mab = math.ceil, math.floor, math.sqrt, math.min, math.max, math.abs local function getgcd(x, y) while 0 < x do x, y = y % x, x end return y end local function getprimes(x) local primes = {} local allnums = {} for i = 1, x do allnums[i] = true end for i = 2, x do if allnums[i] then table.insert(primes, i) local lim = mfl(x / i) for j = 2, lim do allnums[j * i] = false end end end return primes end local function getdivisorparts(x, primes) local prime_num = #primes local tmp = {} local lim = mce(msq(x)) local primepos = 1 local dv = primes[primepos] while primepos <= prime_num and dv <= lim do if x % dv == 0 then local t = {} t.p = dv t.cnt = 1 x = x / dv while x % dv == 0 do x = x / dv t.cnt = t.cnt + 1 end table.insert(tmp, t) lim = mce(msq(x)) end if primepos == prime_num then break end primepos = primepos + 1 dv = primes[primepos] end if x ~= 1 then local t = {} t.p, t.cnt = x, 1 table.insert(tmp, t) end return tmp end local function getdivisorCore(divisorparts) local t = {} local pat = 1 local len = #divisorparts local allpat = 1 for i = 1, len do allpat = allpat * (1 + divisorparts[i].cnt) end for t_i_pat = 0, allpat - 1 do local div = allpat local i_pat = t_i_pat local ret = 1 for i = 1, len do div = mfl(div / (divisorparts[i].cnt + 1)) local mul = mfl(i_pat / div) i_pat = i_pat % div for j = 1, mul do ret = ret * divisorparts[i].p end end table.insert(t, ret) end -- table.sort(t) return t end local function getdivisor(x, primes) local dvp = getdivisorparts(x, primes) return getdivisorCore(dvp) end local n, m, k = io.read("*n", "*n", "*n", "*l") local s = io.read() local b = {} for ss in s:gmatch("%d+") do table.insert(b, tonumber(ss)) end local a = {} for i = 1, n do a[i] = io.read("*n") end if s:sub(1, 1) == "+" then local t = {} for i = 1, m do local rem = b[i] % k if not t[rem] then t[rem] = 1 else t[rem] = t[rem] + 1 end end local ans = 0 for i = 1, n do local rem = a[i] % k rem = (k - rem) % k if t[rem] then ans = ans + t[rem] end end print(ans) os.exit() end local primes = getprimes(33333) local divs = getdivisor(k, primes) local bp = {} for i = 1, #divs do bp[divs[i]] = 0 end for ib = 1, m do local gcd = getgcd(b[ib], k) bp[gcd] = bp[gcd] + 1 end local bpsum = {} for i = 1, #divs do local dv = divs[i] local inv = mfl(k / dv) local invs = getdivisor(inv, primes) local cnt = 0 for i = 1, #invs do cnt = cnt + bp[invs[i] * dv] end bpsum[dv] = cnt end local ans = 0 for ia = 1, n do local gcd = getgcd(a[ia], k) local invgcd = mfl(k / gcd) ans = ans + bpsum[invgcd] end print(ans)