Avoiding Financial Nightmare

Nowadays, taking out a loan from a bank or a financial company has become very common, whether for business or personal purposes. If you manage your spending well, a loan or a credit card can be a great help; otherwise, it can become your worst financial nightmare. A professor has decided to take out a loan to buy a new house in a pleasant city in Indonesia.

Three values affect his monthly bill:

• Principal $N$: the remaining amount of the loan
• Period $M$: the number of months needed to pay off the loan
• Rate $R$: the monthly interest rate (a percentage)

Banks and financial companies usually offer a fixed-payment plan. Every month the customer pays the same amount $T$ (the total monthly payment), which is made up of two parts. Let $P$ be the remaining principal in a given month.

The interest payment $I$ is the rate applied to the remaining principal, rounded up to the nearest integer.

$I = \left\lceil \frac{R \times P}{100} \right\rceil$

The principal payment is the total monthly payment $T$ minus the interest payment, and the remaining principal decreases by that amount.

$P_{\text{new}} = P - (T - I)$

The total monthly payment $T$ must be the same every month, and it must be chosen so that when the period ends the remaining principal is 0 — or, if reaching exactly 0 is impossible, the negative amount nearest to 0. Find that total monthly payment $T$.

For example, with a principal of $42,000, a monthly interest rate of 5%, and a 5-month term, the monthly payment is $9,701.

• Term 1: interest payment = ⌈5% × $42,000⌉ = $2,100, principal payment = $9,701 − $2,100 = $7,601, remaining principal = $42,000 − $7,601 = $34,399
• Term 2: interest payment = ⌈5% × $34,399⌉ = $1,720, principal payment = $9,701 − $1,720 = $7,981, remaining principal = $34,399 − $7,981 = $26,418

After the 5th term the remaining principal is exactly $0.

The input consists of several test cases. Each case is given as three integers $N$, $M$, and $R$.

• $N$ ($1 \le N \le 100{,}000{,}000$): the initial principal
• $M$ ($1 \le M \le 100$): the period in months
• $R$ ($0 \le R \le 100$): the monthly interest rate as a percentage

Process every case until the end of input.

For each case, print the total monthly payment that satisfies the condition on its own line. The value is unique: it is the smallest fixed monthly payment that makes the remaining principal 0, or the negative amount nearest to 0 if 0 is impossible, when the period ends.