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 OCaml (4.02.3) (judge verdict: Accepted)

type drink = {price: int; stock: int};;
let compare_drink d1 d2 = d1.price - d2.price;; 

let input_drink_array n = Array.init n @@ fun _ -> Scanf.scanf " %d %d" @@ fun a b -> {price = a; stock = b};;

let () = Scanf.scanf "%d %d" @@ fun n m -> 
  let drinks = input_drink_array n in (
    Array.fast_sort compare_drink drinks;
    let ans = ref 0 in
    let cnt = ref 0 in (
      for i = 0 to n - 1 do
        if drinks.(i).stock + !cnt < m then (
          ans := !ans + drinks.(i).price * drinks.(i).stock;
          cnt := !cnt + drinks.(i).stock
        ) else if !cnt < m then (
          let rest = m - !cnt in (
            ans := !ans + drinks.(i).price * rest;
            cnt := m;
          )
        )
      done;
      Printf.printf "%d\n" !ans
    )
  )
;;