Task Description
There is a sales coming. Every payment $p$ (a positive integer) will have a discount $d$ according to the following table.
| range of $p$ | discount $d$ | |
|---|---|---|
| 1 | $0 \lt p \lt a$ | 0 |
| 2 | $a \leq p \lt b$ | $v, \text{ if }p\text{ is odd}$ $w, \text{ if }p\text{ is even}$ |
| 3 | $b \leq p$ | $x, \text{ if }p \equiv 0 \pmod{3}$ $y, \text{ if }p \equiv 1 \pmod{3}$ $z, \text{ if }p \equiv 2 \pmod{3}$ |
We define discount rate as $d/p$. Write a program to find the $p$ that has the highest discount rate. If there are multiple payments that give the highest discount rate, output the smallest one.
Input Format
There will be 7 lines for integers $a, b, v, w, x, y, z$.
- $v, w, x, y, z \geq 0$
- $a > 1$
- $b > a + 2$
Output Format
The smallest payment $p$ that has the highest $d/p$ discount rate.
Sample Input
1030561889
Sample Output
10
Hint
Since we have not yet discuss the floating point numbers, so we compare two fractional numbers $a/b$ and $c/d$, by comparing $a * d$ and $b * c$ instead, when both $b$ and $d$ are positive integers.