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 Rust (1.42.0) (judge verdict: Accepted)

use proconio::input;
fn main() {    
    input!{
        n: i64,
        m: i64,
        mut ab: [[i64; 2]; n]
    }
    let mut ans = 0;
    ab.sort();
    ab.iter()
    .try_fold((0, 0), |(acc, sum), x| {
        if acc == m {
            ans = sum;
            None
        }
        else if  acc + x[1] < m{
            let s = sum + x[0]*x[1];
            ans = s;
            Some((acc+x[1], s))
        }
        else{            
            let s = sum + x[0]*(m-acc);
            ans = s;
            Some((m, s))
        }});

    println!{"{}", ans};
}