No.403 2^2^2
りあん
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Problem Statement
For 2^2^2, the result is the same whether it is computed as (2^2)^2 $((2^2)^2 = 4^2 = 16)$ or as 2^(2^2) $(2^{(2^2)} = 2^4 = 16)$, but in general, exponentiation does not satisfy the associative law.
You are given positive integers $A,B,C$ in the form "A^B^C". Find the values of $(A^B)^C$ and $A^{(B^C)}$, and print them on one line, separated by a space.
Since these can be very large numbers, print the remainders when they are divided by $10^9 + 7$.
Input
A^B^C
Positive integers $A,B,C (1 \leq A,B,C \leq 10^{16})$ are given on one line, separated by ' ^ '.
The input contains no extra whitespace.
Output
Print the values of (A^B)^C and A^(B^C), each modulo $10^9 + 7$, on one line, separated by a space.
Print a newline at the end.
Sample
Sample 1
Input
2^2^2
Output
16 16
This is as shown in the problem statement.
Sample 2
Input
2^3^2
Output
64 512
We have $(2^3)^2 = 8^2 = 64$ $,$ $2^{(3^2)} = 2^9 = 512$.
Sample 3
Input
10^10^10
Output
226732710 206165314
Print the remainders when divided by $10^9 + 7$.
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