Geometrical Progression

4000ms

262144K

Description:

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 a₁, a₂, ..., a_n is the geometrical progression, 1 ≤ i, j ≤ n and i ≠ j.

Geometrical progression is a sequence of numbers a₁, a₂, ..., 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 $\text{[math]}$ .

Two progressions a₁, a₂, ..., a_n and b₁, b₂, ..., 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 ≤ 10⁷, 1 ≤ l ≤ r ≤ 10⁷).

Output:

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

Sample Input:

1 1 10

Sample Output:

Sample Input:

2 6 9

Sample Output:

Sample Input:

3 1 10

Sample Output:

Sample Input:

3 3 10

Sample Output:

Note:

These are possible progressions for the first test of examples:

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.

Informação

Provedor Codeforces

Código CF758F