GivenDigitSum | Topcoder Archive

Problem Statement

Given are small positive integers D and S.

Return the smallest positive integer with the following properties:

It has exactly D digits.
The sum of its digits is exactly S.
The product of its digits is zero.

If no such integer exists, return -1 instead.

Definition

Class:: GivenDigitSum
Method:: construct
Parameters:: int, int
Returns:: long
Method signature:: long construct(int D, int S)
(be sure your method is public)

Notes

Everything in this problem is in base 10.
The leading digit of a positive integer must always be non-zero.

Constraints

D will be between 1 and 18, inclusive.
S will be between 1 and 200, inclusive.

Examples

```
1
```
```
7
```
```
Returns: -1
```
The only 1-digit number with sum of digits 7 is obviously the number 7. However, the product of its digits isn't zero (it's 7), so there is no integer with all three required properties.
```
3
```
```
11
```
```
Returns: 209
```
Another integer with all three desired properties is 470: it has 3 digits, its digit sum is 4+7+0 = 11, and its digit product is 4*7*0 = 0. Remember that if multiple integers with the desired properties exist, you must return the smallest one among them. Thus, here only the answer 209 is accepted.
```
18
```
```
1
```
```
Returns: 100000000000000000
```
Watch out for integer overflow. The answer sometimes won't fit into a 32-bit integer variable.
```
11
```
```
11
```
```
Returns: 10000000019
```
```
3
```
```
99
```
```
Returns: -1
```
There is no 3-digit integer with digit sum 99.
```
2
```
```
7
```
```
Returns: 70
```

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