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 C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>

typedef long long int64;

struct shop {
  int64 price;
  int64 number;
};

#ifdef LOCAL
    #define eprintf(...) fprintf(stderr, __VA_ARGS__)
#else
    #define eprintf(...) 42
#endif

#define SWAP(type,a,b) { type temp = a; a = b; b = temp; }
void quicksort(struct shop *arr, int first, int last){
  int i, j, pivot;
  if(first < last){
    pivot = first;
    i = first;
    j = last;
    while(i < j){
      while(arr[i].price <= arr[pivot].price && i < last)
        i++;
      while(arr[j].price > arr[pivot].price)
        j--;
      if(i < j){
        SWAP(struct shop, arr[i],arr[j]);
      }
    }
    SWAP(struct shop, arr[pivot],arr[j]);
    quicksort(arr, first, j - 1);
    quicksort(arr, j + 1, last);
  }
}

void arrdump(struct shop *arr, int len) {
  for (int i = 0; i < len; i++) {
    eprintf("[%d].number = %lld\n", i, arr[i].number);
    eprintf("[%d].price = %lld\n", i, arr[i].price);
  }
}

int main(int argc, const char *argv[])
{
  int n, m;
  scanf("%d%d", &n, &m);
  struct shop s[n];
  for (int i = 0; i < n; i++) {
    scanf("%lld%lld", &s[i].price, &s[i].number);
  }
  quicksort(s, 0, n - 1);
  arrdump(s, n);
  int64 bought = 0;
  int64 sum = 0;
  for (int i = 0; i < n; i++) {
    int64 rest = m - bought - s[i].number;
    if ( rest < 0 ) {
      int64 buy = s[i].number + rest;
      bought += buy;
      eprintf("sum(%lld) += buy(%lld) * [%d].price(%lld)\n", sum, buy, i, s[i].price);
      sum += buy * s[i].price;
      break;
    } else {
      bought += s[i].number;
      sum += s[i].number * s[i].price;
      eprintf("sum(%lld) += [%d].number(%lld) * [%d].price(%lld)\n", sum, i, s[i].number, i, s[i].price);
    }
  }
  printf("%lld\n", sum);

  return 0;
}