Soldier and Bananas

Description

A soldier wants to buy $w$ bananas in the shop. He has to pay $k$ dollars for the first banana, $2k$ dollars for the second one and so on (in other words, he has to pay $i·k$ dollars for the $i$-th banana).

He has $n$ dollars. How many dollars does he have to borrow from his friend soldier to buy $w$ bananas?

Input

The first line contains three positive integers $k, n, w$ ($1  ≤  k, w  ≤  1000$, $0 ≤ n ≤ 10^{9}$), the cost of the first banana, initial number of dollars the soldier has and number of bananas he wants.

Output

Output one integer — the amount of dollars that the soldier must borrow from his friend. If he doesn’t have to borrow money, output $0$.

Examples

Input

3 17 4

Output

13