101212: [AtCoder]ABC121 C - Energy Drink Collector

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.