This new ride at an amusement park is very popular and runs nonstop. The original fee of this ride is price, but it is determined that when using the ride for the Nth time, the fee will increase as N times of the original fee. That is, if the original fee is 100, it will be 200 for the second time, and 300 for the third time.
Write a function solution to return the insufficient money when the ride is used count times.
However, return 0 when the owed amount is sufficient.

Constraints

• Fee of ride price : natural number less than 2,500.
• The initial owned amount money : natural number less than 1,000,000,000.
• The number of rides count : natural number less than 2,500.

Examples

Example #1
The customer has the amount of 20 and wants to use the ride with a fee of 3 four times. The total fee is 30 (= 3+6+9+12), and the insufficient amount is 10. Therefore, return 10.