Restore the Triangle

Limits: 2 sec., 256 MiB

This statement was translated automatically from Ukrainian.

Zenyk drew a triangle on a piece of paper in the morning, but now he has lost it. He only remembers the perimeter of the triangle \(P\) and the radius of its inscribed circle \(r\).

Marichka claims that she can draw a new triangle using this information.

Can you?

Input

The single line contains two positive integers \(P\) and \(r\) — the perimeter of the triangle and the radius of the inscribed circle.

Output

In three lines, output \(x_i\) and \(y_i\) — the coordinates of the vertices of the triangle.

\(|x_i|\) and \(|y_i|\) must not exceed \(10^4\). It is guaranteed that there exists a triangle satisfying such constraints.

Let \(P'\) be the perimeter of your triangle, and \(r'\) be the radius of the circle inscribed in it. The answer will be considered correct if \(\frac{|P'-P|}{P} < 10^{-4}\) and \(\frac{|r'-r|}{r} < 10^{-4}\).

Constraints

\(1 \le P, r \le 10^3\).

Samples

Input (stdin) сopy	Output (stdout) сopy
12 1	0 0 3 0 0 4

Notes

For \(P=12, r = 1\) one of the possible answers is a right-angled triangle with legs \(3\) and \(4\) and hypotenuse \(5\).