Codeforces Round #400 (Div. 1 + Div. 2, combined) 776E. The Holmes Children（待翻译）

2024-05-20 20:50:05

Codeforces Round #241 (Div. 2) 514C Watto and Mechanism

≤,≠，≥＜＞
时间限制：1S / 空间限制：256MB

【在线测试提交传送门】

【问题描述】

The Holmes children are fighting over who amongst them is the cleverest.
Mycroft asked Sherlock and Eurus to find value of f(n), where f(1) = 1 and for n ≥ 2, f(n) is the number of distinct ordered positive integer pairs (x, y) that satisfy x + y = n and gcd(x, y) = 1. The integer gcd(a, b) is the greatest common divisor of a and b.

Sherlock said that solving this was child’s play and asked Mycroft to instead get the value of
.
Summation is done over all positive integers d that divide n.

Eurus was quietly observing all this and finally came up with her problem to astonish both Sherlock and Mycroft.

She defined a k-composite function Fk(n) recursively as follows:

She wants them to tell the value of Fk(n) modulo 1000000007.

【输入格式】

A single line of input contains two space separated integers n (1 ≤ n ≤ 1012) and k (1 ≤ k ≤ 1012) indicating that Eurus asks Sherlock and Mycroft to find the value of Fk(n) modulo 1000000007.

【输出格式】

Output a single integer — the value of Fk(n) modulo 1000000007.

【输入样例1】

7 1

【输出样例1】

【输入样例2】

10 2

【输出样例2】

【样例说明】

In the first case, there are 6 distinct ordered pairs (1, 6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1) satisfying x + y = 7 and gcd(x, y) = 1. Hence, f(7) = 6. So, F1(7) = f(g(7)) = f(f(7) + f(1)) = f(6 + 1) = f(7) = 6.

慎入：以下为解题思路和参考代码，请务必先自行思考！

【解题思路】

【参考代码】

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