# Problem D

Happy Happy Prime Prime

**RILEY VASHTEE**: [*reading from display*] Find the next number in the
sequence:

**313 331 367 ...? What?**

**THE DOCTOR: 379.**

**MARTHA JONES:** What?

**THE DOCTOR:** It’s a sequence of happy
primes – **379**.

**MARTHA JONES:** Happy *what?*

**THE DOCTOR**: Any number that reduces
to one when you take the sum of the square of its digits and
continue iterating it until it yields $1$ is a happy number. Any number that
doesn’t, isn’t. A *happy* prime is both happy and
prime.

**THE DOCTOR**: I dunno, talk about
*dumbing down*. Don’t they teach recreational
mathematics anymore?

Excerpted from “*Dr. Who*,” Episode 42
(2007).

The number 7 is certainly prime. But is it happy?

\begin{eqnarray*} 7 & \rightarrow & 7^2 = 49 \\ 49 & \rightarrow & 4^2 + 9^2 = 97 \\ 97 & \rightarrow & 9^2 + 7^2 = 130 \\ 130 & \rightarrow & 1^2 + 3^2 = 10 \\ 10 & \rightarrow & 1^2 + 0^2 = 1 \\ \end{eqnarray*}It is happy `:-)` As it happens, 7
is the smallest happy prime. Please note that for the purposes
of this problem, 1 is *not* prime.

For this problem you will write a program to determine if a number is a happy prime.

## Input

The first line of input contains a single integer $P$, ($1 \le P \le 10\, 000$), which is the number of data sets that follow. Each data set should be processed identically and independently.

Each data set consists of a single line of input. It contains the data set number, $K$, followed by the happy prime candidate, $m$, ($1 \le m \le 10\, 000$).

## Output

For each data set there is a single line of output. The
single output line consists of the data set number,
$K$, followed by a single
space followed by the candidate, $m$, followed by a single space,
followed by `YES` or `NO`, indicating whether $m$ is a happy prime.

Sample Input 1 | Sample Output 1 |
---|---|

4 1 1 2 7 3 383 4 1000 |
1 1 NO 2 7 YES 3 383 YES 4 1000 NO |