EIU Programming Practices and Exams

Mr. Huy wants to buy a new car worth X VND, so he decided to take out a bank loan with an interest rate of r% per year for N months. He calculates that he could pay a maximum of Y VND per month (includes principal and interest). However, if he pays his loan off early, he will be charged a prepayment penalty fee f%. Your task is to write a program to calculate loan balance every month until the loan balance is 0 (which means he finally pays off the loan).

* Prepayment penalty fee = f% * amount of prepay

Input

The only line contains 3 integers X, Y, N and 2 real numbers r, f (0 < X < 10¹², 0 < N ≤ 500, X/N + X*r/12 ≤ Y < 10¹², 0 < r ≤ 15,  1 ≤ f ≤ 3).

Output

For each month, output the index and the loan balance (rounded to the nearest integer).

Note: Only rounded to show result, not rounded while calculating.

Sample

Explain: https://docs.google.com/spreadsheets/d/1If7TofhSS-Q2trCc09E7iLl7DMZ7gnEhC-IECwChJ2I/edit#gid=0

Note for testcase 1: In the first month, Huy has to pay 12 for interst, 100 for standard monthly payment. There are 188 left that he want to pay, so he prepay 186.1386 plus 1% of it as penalty,