The factorial of a natural number is the product of all positive integers less than or equal to it. For example, the factorial of 4 is 1 · 2 · 3 · 4 = 24. A faulty factorial of length n is similar to the factorial of n, but it contains a fault: one of the integers is strictly smaller than what it should be (but still at least 1). For example, 1 · 2 · 2 · 4 = 16 is a faulty factorial of length 4.</p>

Given the length n, a prime modulus p and a target remainder r, find some faulty factorial of length n that gives the remainder r when divided by p.

입력 형식

The first line contains three integers n, p and r (2 ≤ n ≤ 10¹⁸, 2 ≤ p < 10⁷, 0 ≤ r < p) — the length of the faulty factorial, the prime modulus and the target remainder as described in the problem statement

출력 형식

If there is no faulty factorial satisfying the requirements output “-1 -1”. Otherwise, output two integers — the index k of the fault (2 ≤ k ≤ n) and the value v at that index (1 ≤ v < k). If there are multiple solutions, output any of them.

예제 입력 1

4 5 1

예제 출력 1

3 2

예제 입력 2

4 127 24

예제 출력 2

-1 -1

힌트

In the first example, the output describes the faulty factorial 1 · 2 · 2 · 4 = 2⁴ ≡ 1(mod 5).