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 Kotlin (1.0.0) (judge verdict: Wrong Answer)

import java.util.Scanner

fun main(args: Array<String>) {
    val sc = Scanner(System.`in`)
    val shopCount = sc.nextInt()
    val drinkCount = sc.nextInt()
    val shops = parseList(sc, shopCount)
    val result = buy(drinkCount, shops)
    println(result)
}

private fun parseList(scanner: Scanner, length: Int): List<Pair<Int, Int>> {
    return (0 until length).map {
        val price = scanner.nextInt()
        val size = scanner.nextInt()
        price to size
    }.sortedByDescending { it.first }
}

private tailrec fun buy(targetDrinkCount: Int, shops: List<Pair<Int, Int>>, cost: Long = 0, drinkCount: Long = 0): Long {
    val minShop = shops.last()
    val shouldBuyCount = targetDrinkCount - drinkCount
    return when {
        shouldBuyCount > minShop.second -> {
            // 全て買う
            val tempCost = minShop.first * minShop.second
            buy(targetDrinkCount, shops.dropLast(1), cost + tempCost, drinkCount + minShop.second)
        }
        else -> {
            // 買う個数が決まってる
            val tempCost = minShop.first * shouldBuyCount
            cost + tempCost
        }
    }
}