Description

Given that m and n are integers satisfying the following two conditions:

    ① m, n ∈ {1, 2, ..., k}, i.e., 1 ≤ m, n ≤ k

    ② (n² - m * n - m²)² = 1

    Your task is: Write a program that takes a positive integer k (1 ≤ k ≤ 10⁹) as input and finds a pair (m, n) that satisfies the above two conditions while maximizing the value of m² + n². For example, if the input is k = 1995, the output should be: m=987   n=1597.

Input Format

    </strong>A positive integer k (1 ≤ k ≤ 10⁹).

Output Format

Output m and n, following the sample output.

1995

m=987
n=1597

Source

CodesOnline