218 . 簡單函數

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User's AC Ratio

100.0% (4/4)

Submission's AC Ratio

55.6% (5/9)

Tags

ioicamp ioicamp-2021

Description

定義函數 $f:\mathbb N \to \mathbb N$ 如下： $$ f(x) = \lfloor \log_2 x \rfloor + \lfloor \log_3 x \rfloor + \ldots + \lfloor \log_x x \rfloor. $$ 給定正整數 $N$，請你計算 $f(2) + f(3) + \ldots + f(N)$。請輸出答案模 $10^ 9 + 7$。

Input Format

輸入只有一個正整數 $N$。

  • $1 \leq N \leq 10^ {12}$

Output Format

請輸出一個整數代表答案，答案請模 $10^ 9 + 7$ 後輸出。

Sample Input 1

3

Sample Output 1

3

Sample Input 2

4

Sample Output 2

7

Sample Input 3

100

Sample Output 3

5890

Hints

Problem Source

IOICamp 2021 Day4 pB

Subtasks

No. Testdata Range Constraints Score
1 0~2 範例測資 0
2 0~59 無額外限制 100

Testdata and Limits

No. Time Limit (ms) Memory Limit (VSS, KiB) Output Limit (KiB) Subtasks
0 1000 262144 65536 1 2
1 1000 262144 65536 1 2
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