eCoins
At the Department for Bills and Coins, an extension of today’s monetary system has newly been proposed, in order to make it fit the new economy better. A number of new so called ecoins will be produced, which, in addition to having a value in the normal sense of today, also have an InfoTechnological value. The goal of this reform is, of course, to make justice to the economy of numerous dotcom companies which, despite the fact that they are low on money surely have a lot of IT inside. All money of the old kind will keep its conventional value and get zero InfoTechnological value.
To successfully make value comparisions in the new system, something called the emodulus is introduced. This is calculated as $\sqrt {X^2 + Y^2}$, where $X$ and $Y$ hold the sums of the conventional and InfoTechnological values respectively. For instance, money with a conventional value of $3 altogether and an InfoTechnological value of $4 will get an emodulus of $5. Bear in mind that you have to calculate the sums of the conventional and InfoTechnological values separately before you calculate the emodulus of the money.
To simplify the move to ecurrency, you are assigned to write a program that, given the emodulus that shall be reached and a list of the different types of ecoins that are available, calculates the smallest amount of ecoins that are needed to exactly match the emodulus. There is no limit on how many ecoins of each type that may be used to match the given emodulus.
Input
A line with the number of problems $n$ ($0<n\le 100$), followed by $n$ times:

A line with the integers $m$ ($0<m\le 40$) and $S$ ($0< S \le 300$), where $m$ indicates the number of different ecoin types that exist in the problem, and $S$ states the value of the emodulus that shall be matched exactly.

$m$ lines, each consisting of one pair of nonnegative integers describing the value of an ecoin. The first number in the pair states the conventional value, and the second number holds the InfoTechnological value of the coin. Both values are between $0$ and $S$ (inclusive).
When more than one number are present on a line, they will be separated by a space. Between each problem, there will be one blank line.
Output
The output consists of $n$ lines. Each line contains either a single integer holding the number of coins necessary to reach the specified emodulus $S$ or, if $S$ cannot be reached, the string “not possible”.
Sample Input 1  Sample Output 1 

3 2 5 0 2 2 0 3 20 0 2 2 0 2 1 3 5 3 0 0 4 5 5 
not possible 10 2 