4404: Geometrical Progression
内存限制：256 MB
时间限制：2 S
标准输入输出
题目类型：传统
评测方式：文本比较
上传者：
提交：2
通过：2
题目描述
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≤ai≤r and ai≠aj , where a1,a2,...,an is the geometrical progression, 1≤i,j≤n and i≠j.
Geometrical progression is a sequence of numbers a1,a2,...,an 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 a1,a2,...,an and b1,b2,...,bn are considered different, if there is such i (1≤i≤n) that ai≠bi.
Geometrical progression is a sequence of numbers a1,a2,...,an 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 a1,a2,...,an and b1,b2,...,bn are considered different, if there is such i (1≤i≤n) that ai≠bi.
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.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.
- 6,7;
- 6,8;
- 6,9;
- 7,6;
- 7,8;
- 7,9;
- 8,6;
- 8,7;
- 8,9;
- 9,6;
- 9,7;
- 9,8.
- 1,2,4;
- 1,3,9;
- 2,4,8;
- 4,2,1;
- 4,6,9;
- 8,4,2;
- 9,3,1;
- 9,6,4.
- 4,6,9;
- 9,6,4.
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