Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
F. Geometrical Progression

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputFor given *n*, *l* and *r* find the number of distinct geometrical progression, each of which contains *n* distinct integers not less than *l* and not greater than *r*. In other words, for each progression the following must hold: *l* ≤ *a*_{i} ≤ *r* and *a*_{i} ≠ *a*_{j} , where *a*_{1}, *a*_{2}, ..., *a*_{n} is the geometrical progression, 1 ≤ *i*, *j* ≤ *n* and *i* ≠ *j*.

Geometrical progression is a sequence of numbers *a*_{1}, *a*_{2}, ..., *a*_{n} where each term after first is found by multiplying the previous one by a fixed non-zero number *d* called the common ratio. Note that in our task *d* may be non-integer. For example in progression 4, 6, 9, common ratio is .

Two progressions *a*_{1}, *a*_{2}, ..., *a*_{n} and *b*_{1}, *b*_{2}, ..., *b*_{n} are considered different, if there is such *i* (1 ≤ *i* ≤ *n*) that *a*_{i} ≠ *b*_{i}.

Input

The first and the only line cotains three integers *n*, *l* and *r* (1 ≤ *n* ≤ 10^{7}, 1 ≤ *l* ≤ *r* ≤ 10^{7}).

Output

Print the integer *K* — is the answer to the problem.

Examples

Input

1 1 10

Output

10

Input

2 6 9

Output

12

Input

3 1 10

Output

8

Input

3 3 10

Output

2

Note

These are possible progressions for the first test of examples:

- 1;
- 2;
- 3;
- 4;
- 5;
- 6;
- 7;
- 8;
- 9;
- 10.

These are possible progressions for the second test of examples:

- 6, 7;
- 6, 8;
- 6, 9;
- 7, 6;
- 7, 8;
- 7, 9;
- 8, 6;
- 8, 7;
- 8, 9;
- 9, 6;
- 9, 7;
- 9, 8.

These are possible progressions for the third test of examples:

- 1, 2, 4;
- 1, 3, 9;
- 2, 4, 8;
- 4, 2, 1;
- 4, 6, 9;
- 8, 4, 2;
- 9, 3, 1;
- 9, 6, 4.

These are possible progressions for the fourth test of examples:

- 4, 6, 9;
- 9, 6, 4.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/17/2022 07:21:28 (j1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|