SpecialSquare | Topcoder Archive

Problem Statement

You are given a positive integer N and a very small positive integer C. (C is at most 8.)

Let X be the following number: X = C * (10^N - 1)^2 / 81.

It can be shown that X is always a positive integer too.

We are interested in the (standard base-10) digits of X. You are given two indices A and B. Return the string formed by the A-th to B-th digit of X, inclusive.

(Digits of X are numbered from the left to the right, starting with 1.)

Definition

Class:: SpecialSquare
Method:: substring
Parameters:: int, int, int, int
Returns:: String
Method signature:: String substring(int N, int C, int A, int B)
(be sure your method is public)

Constraints

N will be between 1 and 10^9, inclusive.
C will be between 1 and 8, inclusive.
A will be between 1 and the number of digits in X, inclusive.
B will be between A and the number of digits in X, inclusive.
(B-A) will not exceed 2,500.

Examples

```
3
```
```
1
```
```
1
```
```
5
```
```
Returns: "12321"
```
For N=3 and C=1 we have X=12321. The request is to print the digits of X starting with the first (A=1) and ending with the fifth (B=5), so we print the whole number.
```
3
```
```
1
```
```
2
```
```
5
```
```
Returns: "2321"
```
Same number as Example 0, but now we only return digits at positions 2-5.
```
3
```
```
1
```
```
1
```
```
4
```
```
Returns: "1232"
```
Same number as Example 0, but now we only return digits at positions 1-4.
```
100
```
```
2
```
```
7
```
```
7
```
```
Returns: "5"
```
For N=100 and C=2 the 7-th most significant digit of X is 5.
```
10
```
```
1
```
```
9
```
```
12
```
```
Returns: "0098"
```
Note that sometimes the digit in position A can be a zero, so the string you return may have one or more leading zeros.
```
5
```
```
6
```
```
2
```
```
7
```
```
Returns: "407259"
```
The full X is 740,725,926. We return its second to seventh digit.
```
18
```
```
3
```
```
12
```
```
32
```
```
Returns: "037036962962962962962"
```

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