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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.PriorityQueue;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        try (Scanner sc = new Scanner(System.in)) {
            new Main().solve(sc);
        }
    }

    void solve(Scanner sc) {
        int n = sc.nextInt();
        int m = sc.nextInt();
        PriorityQueue<Shop> shops = new PriorityQueue<>(n, (x, y) -> {
            if (x.price == y.price) {
                return 0;
            } else if (x.price > y.price) {
                return 1;
            } else {
                return -1;
            }
        });

        for (int i = 0; i < n; i++) {
            int a = sc.nextInt();
            int b = sc.nextInt();
            Shop shop = new Shop(a, b);
            shops.add(shop);
        }

        long ans = 0;
        long tmp = 0;
        while (tmp < m) {
            Shop s = shops.poll();
            if (m - tmp >= s.stock) {
                ans += s.price * s.stock;
                tmp += s.stock;
            } else {
                ans += s.price * (m - tmp);
                tmp += m - tmp;
            }
        }
        System.out.println(ans);
    }
}

class Shop {
    public long price;
    public long stock;

    Shop(long price, long stock) {
        this.price = price;
        this.stock = stock;
    }
}