The Holmes Children

2000ms

262144K

Description:

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 $\text{[math]}$ . 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 F_k(n) recursively as follows:

$\text{[math]}$

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

Input:

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 F_k(n) modulo 1000000007.

Output:

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

Sample Input:

7 1

Sample Output:

Sample Input:

10 2

Sample Output:

Note:

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.

Informação

Provedor Codeforces

Código CF776E