Allowance (2) X32391

You have saved $n$ euros. Additionally, every Monday of the next $t$ weeks, you will be given a weekly allowance of $a_1, a_2, ..., a_t$ euros, respectively. Every week, you have a fixed amount of expenses that sums up to $d$ euros.

Write a program that counts how many weeks you end up with a strictly positive balance.

Input

The input consists of three naturals $d \geq 0$, $n \geq 0$ and $t> 0$, which represent fixed weekly expenses, the initial savings, and the number of weeks with allowance, respectively.

Following, there are the quantities corresponding to the $t$ weekly allowances $a_1, ..., a_t$. Every week allowance is a natural number $a_{i}\geq 0$.

Output

The output is a natural number indicating the number of weeks which end up with a strictly positive balance, after paying the weekly expenses.

Your program must meet the output format described in the examples an it should follow a right programming style. You may also decide to include comments, if appropriate.