Problem8995--[yosupo] Number Theory - Kth Root (Mod)

8995: [yosupo] Number Theory - Kth Root (Mod)

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Time Limit : 1.000 sec  Memory Limit : 512 MiB  Special Judge

Description

Each test case consists of $T$ cases.
Given $K, Y, P(P: \textrm{prime})$.
Print any $X$ s.t. $X^K \equiv Y \pmod{P}$, or $-1$ if there is no such $X$.
We note that $0^0\equiv 1 \pmod{P}$ in this problem.

Input

$T$
$K_0$ $Y_0$ $P_0$
$K_1$ $Y_1$ $P_1$
$\vdots$
$K_{T-1}$ $Y_{T-1}$ $P_{T-1}$

Output

For each line, print $X$ or $-1$.

Constraints

$1 \leq T \leq @{param.T_MAX}$
$0 \leq K \leq @{param.K_MAX}$
$2 \leq P \leq @{param.P_MAX}$
$0 \leq Y  < P$
$P$ is prime

Sample 1 Input

5
0 10 11
10 9 11
1 1 2
5 4 13
0 8 11

Sample 1 Output

-1
-1
1
10
-1

HINT

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