Problem:
Score : 300 points

Problem Statement

Hearing that energy drinks increase rating in those sites, Takahashi decides to buy up M cans of energy drinks.

There are N stores that sell energy drinks. In the i-th store, he can buy at most B_i cans of energy drinks for A_i yen (the currency of Japan) each.

What is the minimum amount of money with which he can buy M cans of energy drinks?

It is guaranteed that, in the given inputs, a sufficient amount of money can always buy M cans of energy drinks.

Constraints

All values in input are integers.

1 \leq N, M \leq 10^5

1 \leq A_i \leq 10^9

1 \leq B_i \leq 10^5

B_1 + ... + B_N \geq M

Input

Input is given from Standard Input in the following format:

N M
A_1 B_1
A_2 B_2
\vdots
A_N B_N

Output

Print the minimum amount of money with which Takahashi can buy M cans of energy drinks.

Sample Input 1

2 5
4 9
2 4

Sample Output 1

12

With 12 yen, we can buy one drink at the first store and four drinks at the second store, for the total of five drinks. However, we cannot buy 5 drinks with 11 yen or less.

Sample Input 2

4 30
6 18
2 5
3 10
7 9

Sample Output 2

130

Sample Input 3

1 100000
1000000000 100000

Sample Output 3

100000000000000

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

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

#-swank
(unless (member :child-sbcl *features*)
  (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))))
(defmacro dp (name args memo-size &body body)
  (let ((memo (gensym)))
    `(let ((,memo (make-array ,memo-size :initial-element nil)))
       (defun ,name ,args
         (or (aref ,memo ,@args)
             (setf (aref ,memo ,@args)
                   ,@body))))))

(defun split (x str)
  (let ((pos (search x str))
        (size (length x)))
    (if pos
      (cons (subseq str 0 pos)
            (split x (subseq str (+ pos size))))
      (list str))))

(defmacro collect-times (time body)
  `(loop repeat ,time collect ,body))

(defun read-times (time)
  (collect-times time (read)))

(defun main (m shops)
  (loop for shop in (sort shops (lambda (a b) (< (car a) (car b))))
        until (zerop m)
       sum 
           (progn
             (let ((buy (min m (cdr shop))))
               (decf m buy)
               (* buy (car shop))))))

(let* ((n (read))
       (m (read))
       (shops (collect-times n (cons (read) (read)))))
  (princ (main m shops)))