my Lua code which fails some tests

local sqrt = math.sqrt

--  array of primes
local primes = setmetatable({2, 3, 5}, {__index =
   function(t, k)
      local p = t[#t]
      for k = #t + 1, k do
         repeat
            p = p + 4 * p % 6
            local i, root, is_compound = 2, sqrt(p) - 1.5
            repeat
               i = i + 1
               local pp = t[i]
               is_compound = p % pp == 0
            until is_compound or root < pp
         until not is_compound
         t[k] = p
      end
      return p
   end
})
local _ = primes[100000]   -- precalculate all p_k (it takes 1.2 seconds)


local function Z_inv(value) -- -- 0 <= value < 1000000007
   -- returns value^(-1) mod 1000000007
   -- returns nothing if value = 0
   local b, s, p, n = 1000000007, value, 0, 1
   while s > 1 do
      local r = b % s
      p, n = n, p + (r - b) / s * n
      b, s = s, r
   end
   if s == 1 then
      return n % 1000000007
   end
end

local function Z_mul(A, B)  -- 0 <= A, B < 1000000007
   local R = B % 65536
   return ((B - R) / 65536 * A % 1000000007 * 65536 + A * R) % 1000000007
end

local G = setmetatable({[0] = 1}, {__index =
   function(t, k)
      local g = t[#t]
      for k = #t + 1, k do
         local ii = Z_inv(primes[k]-1)
         g = Z_mul(g, Z_mul(ii, ii))
         t[k] = g
      end
      return g
   end
})
local _ = G[100000]   --  precalculate all G[m] (it takes only 0.15 sec)

--~ io.input("input.txt")

-------------------------------------------------------------------------------------
--  MAIN LOOP
-------------------------------------------------------------------------------------
-- We have 10+ seconds remaining for the following loop

for _ = 1, io.read"*n" do
   local m, a = io.read("*n", "*n")
   local result = G[m]       -- this value has already been precalculated
   for k = 1, m do
      ------------------------------------------------------------------------
      -- The body of this inner loop is executed up to 3.9 million times
      -- I need to increase its speed by 11% to pass all test cases
      -- But I don't know how optimize it more
      ------------------------------------------------------------------------
      local p = primes[k]    -- this value has already been precalculated
      local ak2 = a + k + 2  -- 3 <= ak2 < 2^18
      -- Next 16 lines calculate:  W = p^ak2
      local exponent = ak2
      local mask = 131072    -- 2^17
      while mask > exponent do
         mask = mask / 2
      end
      exponent = exponent - mask
      local W = p
      while mask > 1 do
         local R = W % 65536
         W = ((W - R) / 65536 * W % 1000000007 * 65536 + W * R) % 1000000007
         mask = mask / 2
         if exponent >= mask then
            exponent = exponent - mask
            W = W * p % 1000000007
         end
      end
      -- Next 3 lines calculate:  result = result * (W - 1 - (p - 1) * ak2)
      local W = (W - 1 - (p - 1) * ak2) % 1000000007
      local R = W % 65536
      result = ((W - R) / 65536 * result % 1000000007 * 65536 + result * R) % 1000000007
      ------------------------------------------------------------------------
   end
   print(result)
end

--~ print(os.clock())