Problem:
Fractional Knapsack Problem

You have $N$ items that you want to put them into a knapsack of capacity $W$. Item $i$ ($1 \le i \le N$) has weight $w_i$ and value $v_i$ for the weight.

When you put some items into the knapsack, the following conditions must be satisfied:

The total value of the items is as large as possible.

The total weight of the selected items is at most $W$.

You can break some items if you want. If you put $w'$($0 \le w' \le w_i$) of item $i$, its value becomes $\displaystyle v_i \times \frac{w'}{w_i}.$

Find the maximum total value of items in the knapsack.

Input

$N$ $W$
$v_1$ $w_1$
$v_2$ $w_2$
:
$v_N$ $w_N$

The first line consists of the integers $N$ and $W$. In the following $N$ lines, the value and weight of the $i$-th item are given.

Output

Print the maximum total value of the items in a line. The output must not contain an error greater than $10^{-6}$.

Constraints

$1 \le N \le 10^5$

$1 \le W \le 10^9$

$1 \le v_i \le 10^9 (1 \le i \le N)$

$1 \le w_i \le 10^9 (1 \le i \le N)$

Sample Input 1

3 50
60 10
100 20
120 30

Sample Output 1

240

When you put 10 of item $1$, 20 of item $2$ and 20 of item $3$, the total value is maximized.

Sample Input 2

3 50
60 13
100 23
120 33

Sample Output 2

210.90909091

When you put 13 of item $1$, 23 of item $2$ and 14 of item $3$, the total value is maximized. Note some outputs can be a real number.

Sample Input 3

1 100
100000 100000

Sample Output 3

100

Solution in C (judge verdict: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>

#define BUF_SIZE 25

struct product {
  int weight;
  double value;
  int total_value;
};

int comp(const void *a, const void *b) {
  return ((struct product*)a)->value < ((struct product*)b)->value;
}

int main(void) {
  FILE *fp = stdin;
  char line[BUF_SIZE];
  if(!fgets(line, BUF_SIZE, fp)) return 0;
  int num, weight;
  sscanf(line, "%d %d", &num, &weight);

  struct product *prods = malloc(sizeof(struct product)*num);

  int i, j;
  for(i = 0; i < num; i++) {
    if(!fgets(line, BUF_SIZE, fp)) return 0;
    int val, wei;
    sscanf(line, "%d %d", &val, &wei);
    prods[i].weight = wei;
    prods[i].value = (double)val/(double)wei;
    prods[i].total_value = val;
  }

  qsort(prods, num, sizeof(struct product), comp);
  int cur_weight = 0;
  double sum = 0;
  for(i = 0; i < num; i++) {
    int rem = weight - cur_weight;
    if(rem > prods[i].weight) {
      cur_weight += prods[i].weight;
      sum += prods[i].total_value;
    } else {
      sum += prods[i].value * rem;
      break;
    }
  }
  printf("%lf\n", sum);
  return 0;
}