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: Time Limit Exceeded)

let rec qsort compare ls =
  if ls = [] then []
  else
    let p, tl = (List.hd ls), (List.tl ls) in
    let left = List.filter (compare p) tl in
    let right = List.filter (fun x -> not @@ compare p x) tl in
    (qsort compare left) @ p::(qsort compare right)

let rec aux m cash drinks shops =
  if drinks >= m then cash
  else
    let a, b = List.hd shops in
    let shops = List.tl shops in
    if m - drinks >= b then aux m (cash + a * b) (drinks + b) shops
    else if m - drinks < b then aux m (cash + a * (m - drinks)) m shops
    else assert false 

let _ =
  let n, m = Scanf.scanf "%d %d\n" (fun n m -> (n, m)) in
  let pairs = ref [] in
  for i=1 to n do
    Scanf.scanf "%d %d\n" (fun a b -> pairs := (a, b)::!pairs)
  done;
  !pairs
  |> qsort (fun (a, _) (a', _) -> a >= a')
  |> aux m 0 0
  |> print_int