Energy Drink Collector

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.

Examples

Input

2 5 4 9 2 4

Output

12

Input

4 30 6 18 2 5 3 10 7 9

Output

130

Input

1 100000 1000000000 100000

Output

100000000000000

inputFormat

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

outputFormat

Output

Print the minimum amount of money with which Takahashi can buy M cans of energy drinks.

Examples

Input

2 5 4 9 2 4

Output

12

Input

4 30 6 18 2 5 3 10 7 9

Output

130

Input

1 100000 1000000000 100000

Output

100000000000000

样例

4 30
6 18
2 5
3 10
7 9

130