Problem:
Score : 100 points

Problem Statement

There are N items, numbered 1, 2, \ldots, N.
For each i (1 \leq i \leq N), Item i has a weight of w_i and a value of v_i.

Taro has decided to choose some of the N items and carry them home in a knapsack.
The capacity of the knapsack is W, which means that the sum of the weights of items taken must be at most W.

Find the maximum possible sum of the values of items that Taro takes home.

Constraints

All values in input are integers.

1 \leq N \leq 100

1 \leq W \leq 10^5

1 \leq w_i \leq W

1 \leq v_i \leq 10^9

Input

Input is given from Standard Input in the following format:

N W
w_1 v_1
w_2 v_2
:
w_N v_N

Output

Print the maximum possible sum of the values of items that Taro takes home.

Sample Input 1

3 8
3 30
4 50
5 60

Sample Output 1

90

Items 1 and 3 should be taken.
Then, the sum of the weights is 3 + 5 = 8, and the sum of the values is 30 + 60 = 90.

Sample Input 2

5 5
1 1000000000
1 1000000000
1 1000000000
1 1000000000
1 1000000000

Sample Output 2

5000000000

The answer may not fit into a 32-bit integer type.

Sample Input 3

6 15
6 5
5 6
6 4
6 6
3 5
7 2

Sample Output 3

17

Items 2, 4 and 5 should be taken.
Then, the sum of the weights is 5 + 6 + 3 = 14, and the sum of the values is 6 + 6 + 5 = 17.

Solution in Common Lisp (SBCL 2.0.3) (judge verdict: Time Limit Exceeded)

(unless (member :child-sbcl *features*)
  #-swank (quit
            :unix-status
            (process-exit-code
              (run-program *runtime-pathname*
                           `("--control-stack-size" "128MB"
                             "--noinform"
                             "--disable-ldb"
                             "--lose-on-corruption"
                             "--end-runtime-options"
                             "--eval" "(push :child-sbcl *features*)"
                             "--script" ,(namestring *load-pathname*))
                           :output t :error t :input t))))

(eval-when (:compile-toplevel)
  #-swank (proclaim '(optimize (speed 3) (debug 0) (safety 0))))

(eval-when (:compile-toplevel :load-toplevel :execute)
  (labels ((array-reference-reader (stream c n)
             "Reader macro #&(array index) => (aref array index)"
             (declare (ignore c n))
             (let ((list (read stream)))
               `(aref ,(car list) ,@(cdr list)))))
    (setf *readtable* (copy-readtable))
    (set-dispatch-macro-character #\# #\& #'array-reference-reader)))

(defconstant mod-number 1000000007)
(defconstant inf 2000000000)

(defmacro let-if (var cond tbody &optional fbody)
  `(let ((,var ,cond))
     (if ,var
         ,tbody
         ,fbody)))

(defun unfold (p f g seed &optional (tail-gen (lambda () '())))
  (if (p seed)
      (tail-gen seed)
      (cons (f seed)
            (unfold p f g (g seed) tail-gen))))

(defun iota (c &optional (s 0) (step 1) (acc nil))
  (if (zerop c)
      (nreverse acc)
      (iota (1- c) (+ s step) step (cons s acc))))

(defun sum (list &optional (init 0))
  (reduce #'+ list :initial-value init))

(defun chomp (str)
  (string-right-trim '(#\Return #\Linefeed) str))

(defun read-integer (&optional (in *standard-input*))
  (declare (inline read-byte))
  (labels ((number-char-p (b)
             (<= #.(char-code #\0) b #.(char-code #\9)))
           (minus-char-p (b)
             (= b #.(char-code #\-)))
           (to-number (b)
             (- b #.(char-code #\0))))
    (declare (inline number-char-p minus-char-p to-number))
    (macrolet ((%read-byte ()
                 '(the (unsigned-byte 8)
                       #+swank (char-code (read-char in nil #\Nul))
                       #-swank (read-byte in nil 0))))
      (let* ((minus-p nil)
             (x (loop for b = (%read-byte)
                      if (number-char-p b)
                        return (to-number b)
                        end
                      if (minus-char-p b)
                        do (setf minus-p t))))
        (declare (boolean minus-p) (fixnum x))
        (the fixnum (loop for b = (%read-byte)
                          and y = x then (+ (* y 10) (to-number b))
                          unless (number-char-p b)
                            return (funcall (if minus-p #'- #'+) y)))))))

(defun split (x str &optional (acc nil))
  (let ((pos (search x str))
        (size (length x)))
    (if pos
        (split x (subseq str (+ pos size)) (cons (subseq str 0 pos) acc))
        (nreverse (cons str acc)))))

(defmacro minf (field &rest x)
  `(setf ,field (min ,field ,@x)))

(defmacro maxf (field &rest x)
  `(setf ,field (max ,field ,@x)))

(defmacro debug-print (x)
  `(let ((y ,x))
    (format t "~A: ~A~%" ',x y)
    y))

(defmacro defdp (name args &body body)
  (let ((argc (length args))
        (key (gensym)))
    `(let ((dp (make-hash-table :test #'equal)))
       (defun ,name ,args
         (let ((,key ,@(if (= argc 1) args `((list ,@args)))))
           (let-if memo (gethash ,key dp)
                   memo
                   (setf (gethash ,key dp)
                         (progn ,@body))))))))

(defparameter n (read-integer))
(defparameter w-max (read-integer))
(defparameter w (make-array n))
(defparameter v (make-array n))
(dotimes (i n)
  (setf #&(w i) (read-integer))
  (setf #&(v i) (read-integer)))

(defdp solve (index weight)
  (cond ((< weight 0) (- inf))
        ((< index 0) 0)
        (t (max (+ (solve (1- index) (- weight #&(w index)))
                   #&(v index))
                (solve (1- index) weight)))))

(format t "~A~%" (solve (1- n) w-max))