ProdCalc | Topcoder Archive

Problem Statement

You have a calculator that can only handle numbers with up to d digits. Initially, the number shown on the screen is 1. You must perform exactly op multiplication operations. Each operation multiplies the number on the screen by a digit between 2 and 9, inclusive. The result of each operation must be a number with d or less digits. Return the largest number that can be displayed on the screen after op operations. If there is no way to perform op operations without overflowing the calculator, return -1.

Definition

Class:: ProdCalc
Method:: highest
Parameters:: int, int
Returns:: long
Method signature:: long highest(int d, int op)
(be sure your method is public)

Constraints

d will be between 2 and 8, inclusive.
op will be between 0 and 30, inclusive.

Examples

```
4
```
```
3
```
```
Returns: 729
```
The calculator can store up to 4 digits. With 3 multiplications, we can obtain at most 729, by using digit 9 every time: 1 * 9 * 9 * 9 = 729.
```
8
```
```
0
```
```
Returns: 1
```
No multiplications can be performed.
```
2
```
```
3
```
```
Returns: 98
```
The storage is limited to 2 digits. The highest number that can be shown on screen after 3 multiplications is 98 (2 * 7 * 7).
```
8
```
```
10
```
```
Returns: 99574272
```
```
8
```
```
20
```
```
Returns: 99532800
```
```
8
```
```
30
```
```
Returns: -1
```
Even if we would only use digit 2 every time, 2^30 has more than 8 digits and overflows the calculator.
```
2
```
```
6
```
```
Returns: 96
```
```
3
```
```
1
```
```
Returns: 9
```

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