A10668. Geometrical Progression

For 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 $a_{i}≠b_{i}$ .

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

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

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:

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