Czech ACM Student Chapter

Czech Technical University in Prague

Charles University in Prague

Technical University of Ostrava

ˇ a

Slovak University of Technology

Pavol Jozef Saf´rik University in Koˇice

s

ˇ

University of Zilina

Masaryk University

Matej Bel University in Bansk´ Bystrica

a

University of West Bohemia

CTU Open Contest 2011

Intergalactic Mortgage

mortgage.c, mortgage.C, mortgage.java, mortgage.p

Many people on Earth want to solve their housing. When they have not enough money to

buy their house or flat, they get mortgage∗ from some bank and then they pay fixed monthly

payments until they redeem the mortgage.

You may think that paying mortgage for 30 years is a long time, but that is quite short time

compared to galactic mortgages. Aliens are not buying houses, but whole planets. Since planets

are a "little" more expensive, the mortgage periods are longer.

The mortgages work the same way for aliens as for us earthlings. If an alien wants to buy

a planet, he comes to GCB (Galactic Central Bank) to borrow an amount of X . Bank offers

a mortgage with the interest rate r% p.a. (= "per year"). Interests are computed at the end of

each month (1 alien year has 12 months). At the end of every month, the current debt is raised

by (r/12)% and then the alien pays back to bank some fixed amount Y , which is subtracted

from the debt.

Because of intergalactic financial crisis, bank rules are quite strict. Every mortgage must start

on the first day of a year. If an alien does not pay enough money to cover the principal and

interests within first N years, the bank will then confiscate his planet.

On the other hand, galactic employment works quite nice. Once you have a job, you are

guaranteed to have it forever. An alien can give the same amount Y at the end of each month

for the whole mortgage period.

Your task is to decide whether an alien is able to pay his mortgage or not.

Input Specification

The input contains several test cases. Each test case is described by a line containing numbers

X , Y , N , r separated by space. X is principal (the initial amount borrowed), Y is the monthly

payment (paid at the end of each month), N is number of years in which the alien is required

to pay the mortgage, r is interest rate p.a. in percent.

X , Y are integer numbers (1 ≤ X, Y ≤ 1 000 000 000). N is integer number (1 ≤ N ≤ 10 000).

r is float (0 ≤ r ≤ 100, 2 digits precision). Values X , Y , N , r for each test case were chosen so

that even if the alien would not pay anything for the whole time, the resulting debt after N year

would be at most 1025. Also, the precision of double should be sufficient for most computations

(differences in the rate less then 10-8% will not affect the result).

The last test case is followed by a line containing four zeros.

∗

hypot´ka

e

Output Specification

For each test case output "YES" if the alien can pay the mortgage within N years and "NO" if

his salary is too small to pay the mortgage on time.

Sample Input

10000 500

2 5.00

10000 400

2 5.00

10000 245

100 30.00

321321321

2895492 11 3.23

0000

Output for Sample Input

YES

NO

NO

NO