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 PHP7 (7.0.15) (judge verdict: Accepted)


<?php

function check($a, $b, $c)
{
    $sum = 0;
    for ($i = 0; $i < count($a); $i++) {
        $sum += $a[$i] * $b[$i];
    }

    return $sum + $c > 0;
}

// 入力
fscanf(STDIN, "%d %d", $n, $m);

$v = [];
$shops = [];
for ($i = 0; $i < $n; $i++) {
    $str = fgets(STDIN);
    $s = array_map('intval', explode(' ', $str));
    $v[] = $s[0];
    $shops[] = [
        'value' => $s[0],
        'limit' => $s[1],
    ];
}

// A を安い順にソート
array_multisort($v, SORT_ASC, $shops);

// M 本になるまで金額を足していく
$yen = 0;
$count = 0;

$shopIndex = 0;
$shopCount = 0;

while ($count < $m) {
    if ($shopCount < $shops[$shopIndex]['limit']) {
        $yen += $shops[$shopIndex]['value'];
        $count++;
        $shopCount++;
    } else {
        $shopIndex++;
        $shopCount = 0;
    }
}

# 出力
echo $yen . "\n";