The series, 1¹ + 2² + 3³ + ... + 10¹⁰ = 10405071317.

Find the last ten digits of the series, 1¹ + 2² + 3³ + ... + 1000¹⁰⁰⁰.

+-;pow
(defn pow [a b]
  (loop [res 1 mult a shift b]
    (if (= 0 shift)
      res
      (if (= 1 (rem shift 2))
        (recur (* res mult) (* mult mult) (bit-shift-right shift 1))
        (recur res (* mult mult) (bit-shift-right shift 1))
      )
    )
  )
)

+-;pow-mod
(defn pow-mod [a b m]
  (loop [res 1 mult a shift b]
    (if (= 0 shift)
      (rem res m)
      (if (= 1 (rem shift 2))
        (recur (rem (* res mult) m) (rem (* mult mult) m) (bit-shift-right shift 1))
        (recur res (rem (* mult mult) m) (bit-shift-right shift 1))
      )
    )
  )
)

(defn p48 []
  (println
    (let [mod (pow 10 10)]
      (rem (apply + (map #(pow-mod % % mod) (range 1 1001))) mod)
    )
  )
)

+-%pow
pow(_,0)->1;
pow(1,_)->1;
pow(A,B)->pow(A,B,1).
pow(_,0,Res)->Res;
pow(Mult,B,Res) when B band 1 == 1 ->
	pow(Mult*Mult,B bsr 1, Res*Mult);
pow(Mult,B,Res)->pow(Mult*Mult,B bsr 1, Res).

+-%pow_mod
pow_mod(_,_,1)->0;
pow_mod(_,0,_)->1;
pow_mod(1,_,_)->1;
pow_mod(A,B,M)->pow_mod(A,B,M,1).
pow_mod(_,0,_,Res)->Res;
pow_mod(Mult,B,M,Res) when B band 1 ==1 ->
	pow_mod((Mult*Mult) rem M, B bsr 1, M, (Res*Mult) rem M);
pow_mod(Mult,B,M,Res)->pow_mod((Mult*Mult) rem M, B bsr 1, M, Res).

p48()->
	M=pow(10,10),
	io:format("~w~n",[lists:sum(lists:map(fun(X)->pow_mod(X,X,M) end, lists:seq(1,1000))) rem M]).

+-#power_mod
def power_mod(a,b,m)
  b=b.to_s(2).reverse.split("").map{|c| c=="1"}
  acc=1
  while(b.length>0)
    c=b.shift
    acc=(acc*a)%m if c
    a=(a**2)%m
  end
  acc
end

def p48
  p=10**10
  puts (1..1000).map{|i|power_mod(i,i,p)}.sum%p
end