Contest Duration: - (local time) (100 minutes) Back to Home
C - Energy Drink Collector /

Time Limit: 2 sec / Memory Limit: 1024 MB

問題文

なお、与えられる入力では、十分なお金があれば M 本の栄養ドリンクを買い集められることが保証されます。

制約

• 入力は全て整数である。
• 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

入力

N M
A_1 B_1
A_2 B_2
\vdots
A_N B_N


出力

M 本の栄養ドリンクを買い集めるのに必要な最小の金額を出力せよ。

入力例 1

2 5
4 9
2 4


出力例 1

12


12 円あれば 1 軒目の店で 1 本、2 軒目の店で 4 本の栄養ドリンクを購入し、合計 5 本の栄養ドリンクを買い集めることができます。一方、11 円以下では 5 本の栄養ドリンクを買い集めることができません。

入力例 2

4 30
6 18
2 5
3 10
7 9


出力例 2

130


入力例 3

1 100000
1000000000 100000


出力例 3

100000000000000


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.