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 Python (3.4.3) (judge verdict: Accepted)

import numpy as np

N, M = map(int, input().split())
AB = []
for i in range(N):
    AB.append(list(map(int, input().split())))
    
AB = np.array(AB)
AB_sorted = AB[AB[:,0].argsort(),:]

cs = np.cumsum(AB_sorted[:,1])
n_full_store = (cs <= M).sum()
money_a = np.sum(AB_sorted[:n_full_store,0] * AB_sorted[:n_full_store,1])
if M - cs[n_full_store-1] > 0:
    money_b = (M - cs[n_full_store-1]) * AB_sorted[n_full_store,0]
elif M - cs[n_full_store-1] < 0:
               money_b = AB_sorted[0,0] * M
else:
    money_b = 0
print(money_a + money_b)