Your younger brother's teacher gave him this simple problem.

Given b and c. Evaluate the result of this expression:

Result₁ = b^c

Your brother definitely was able to solve this easy problem. So his teacher decided to give him a bit harder problem.

Given a,b and c. Evaluate the result of this expression:

Result₁ = b^c

Result₂ = a^Result1

However, your brother was also able to solve it. It was not that harder. His teacher was excited -though- and gave him this Bonus Programming Assignment.

Write a program that is given a,b and c; calculates the value of Result₂. Since the output may be exponentially very large, checking the correctness of solutions will be a bit subtle problem. So, instead of printing the whole value of Result₂, just print the reaminder of dividing Result₂ by 1,000,000,007 (10⁹ + 7).

Can you help him solve that task?

Input

The input consists of several test cases. Each case is on a single line. In each case, given three space separated integers a,b and c (0 <=a, b, c <= 2³¹ - 1). The input is terminated by a = b = c =  - 1

Output

For each case, print exactly one line containing the value of Result₂ modulus 10⁹ + 7

Input

2 2 2
3 4 5
-1 -1 -1

Output

16
763327764