A cake fit for a king ~wleung_bvg.

Everybody knows that cake comes in two shapes, circular or rectangular.
Everybody except for Wesley.

In his defence:

You wouldn't buy a rectangular shaped pizza would you?

Thus Wesley has only ever cut his cake in one way.

• Imagine a Cartesian grid over the center of the cake labelled at ~(0,0)~.
• Make ~M~ cuts over the line formed by ~y=m_i x~ within the cake's boundaries.

With Wesley's birthday coming up, his friends have decided to play a little prank on him. They have purchased a square shaped cake with side length ~2N~ and would like to know the side length of the largest axis-aligned square obtainable that does not intersect with any cut. A square intersects a cut if there is a non-zero area of the square on both sides of the cut. This means that touching a cut does not count as an intersection.

Slope will be given as ~a_i, b_i~ where ~m_i = \dfrac{a_i}{b_i}~.

Input Specification

The first line will contain two integers, ~N~ and ~M~ ~(1 \le N \le 10^3, 1 \le M \le 10^5)~, half the length of the cake, and the number of cuts Wesley makes.

The next ~M~ lines will each contain two integers, ~a_i, b_i~ ~(1 \le |a_i|, b_i \le 10^3)~, the numerator and denominator of the slope of the line used to determine the cut. ~a_i~ and ~b_i~ are guaranteed to be coprime, and the pair ~(a_i, b_i)~ is guaranteed to be unique.

Output Specification

Output two positive integers, ~n~ and ~d~ space-separated on one line. This means the side length of the largest obtainable axis-aligned square is ~\dfrac n d~. Note that ~n~ and ~d~ must be coprime.

Constraints

Subtask 1 [30%]

~M \le 2~

Subtask 2 [70%]

No additional constraints.

Sample Input 1

1 2
-1 1
1 1

Sample Output 1

2 3

Explanation For Sample 1

The following image shows the cake:

The red square is the cake, and the blue and green lines show the two cuts. The black line shows one of the many different largest squares obtainable.

Sample Input 2

2 2
-1 2
1 1

Sample Output 2

3 2

Sample Input 3

1000 2
-1000 1
1000 1

Sample Output 3

2000000 2001