ConcatenateNumbers | Topcoder Archive

Problem Statement

For two positive integers a and b (a <= b) we define an integer f(a,b) as a concatenation of numbers a, a + 1, a + 2, ..., b - 1, b in a decimal notation. For example, f(2,5) = 2345, f(18,23) = 181920212223.

You are given three ints L, R, v. Return the number of pairs of integers x, y (L <= x <= y <= R) such that f(x,y) is equal to v modulo 1,000,000,007.

Definition

Class:: ConcatenateNumbers
Method:: numberOfSegments
Parameters:: int, int, int
Returns:: long
Method signature:: long numberOfSegments(int L, int R, int v)
(be sure your method is public)

Constraints

L and R will be between 1 and 1,000,000,000 (10^9), inclusive.
R-L will be between 0 and 100,000, inclusive.
v should be between 0 and 1,000,000,006, inclusive.

Examples

```
11
```
```
13
```
```
111213
```
```
Returns: 1
```
f(11,11) = 11, f(11,12) = 1112, f(11,13) = 111213, f(12,12) = 12, f(12,13) = 1213, f(13,13) = 13. You must return 1 because only f(11,13) = 111213 module 1,000,000,007.
```
11
```
```
13
```
```
11213
```
```
Returns: 0
```
```
11
```
```
13
```
```
14
```
```
Returns: 0
```
```
1
```
```
100000
```
```
12345
```
```
Returns: 10
```
```
999900001
```
```
1000000000
```
```
0
```
```
Returns: 7
```

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