Ginkgo Numbers

Ginkgo Numbers

We will de ne Ginkgo numbers and multiplication on Ginkgo numbers.

A Ginkgo number is a pair <m, n> where m and n are integers. For example, <1, 1>, <-2, 1> and <-3, -1> are Ginkgo numbers.

The multiplication on Ginkgo numbers is de ned by <m, n>·<x, y> = <mx-ny, my+nx>.

For example, <1, 1>·<-2, 1> = <-3, -1>.

A Ginkgo number <m, n> is called a divisor of a Ginkgo number <p, q> if there exists a Ginkgo number <x, y> such that <m, n>·<x, y> = <p, q>.

For any Ginkgo number <m, n>, Ginkgo numbers <1, 0>, <0, 1>, <-1, 0>, <0, -1>, <m, n>, <-n, m>, <-m, -n> and <n, -m> are divisors of <m, n>. If m2+n2 > 1, these Ginkgo numbers are distinct. In other words, any Ginkgo number such that m2 + n2 > 1 has at least eight divisors.

A Ginkgo number <m, n> is called a prime if m2+n2 > 1 and it has exactly eight divisors. Your mission is to check whether a given Ginkgo number is a prime or not.

The following two facts might be useful to check whether a Ginkgo number is a divisor of another Ginkgo number.

  • Suppose m2 + n2 > 0. Then, <m, n> is a divisor of <p, q> if and only if the integer m2 + n2 is a common divisor of mp + nq and mq - np.
  • If <m, n>·<x, y> = <p, q>, then (m2 + n2)(x2 + y2) = p2 + q2.


The first line of the input contains a single integer, which is the number of datasets. The rest of the input is a sequence of datasets. Each dataset is a line containing two integers m and n, separated by a space. They designate the Ginkgo number <m, n>. You can assume 1 < m2 + n2 < 20000.


For each dataset, output a character 'P' in a line if the Ginkgo number is a prime. Output a character 'C' in a line otherwise.

Time limit 30 seconds
Memory limit 128 MiB
Input example #1
10 0
0 2
-3 0
4 2
0 -13
-4 1
-2 -1
3 -1
Output example #1
Source ACM International Collegiate Programming Contest, Asia Regional Contest, Tokyo, 2012-11-18