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 = 2 x = mfl(x / dv) while x % dv == 0 do x = mfl(x / dv) t.cnt = t.cnt + 2 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, 2 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 = 1LL 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 p, q = io.read("*n", "*n") local gcd = getgcd(p, q) p = mfl(p / gcd) q = mfl(q / gcd) local primes = getprimes(32000) local dv = getdivisor(q, primes) local pl = 1LL * p local ans = {} for i = 1, #dv do local x = dv[i] + q local y = (1LL * q * q) / dv[i] + q if 0LL < x and 0LL < y and x % pl == 0LL and y % pl == 0LL then table.insert(ans, {x / pl, y / pl}) end end table.sort(ans, function(x, y) return x[1] < y[1] end) print(#ans) for i = 1, #ans do local x = tostring(ans[i][1]):gsub("LL", "") local y = tostring(ans[i][2]):gsub("LL", "") print(x .. " " .. y) end