Anka had a dream in which she and Petka were in the Flat World near a planet called Ocean. This planet was a water disk centered at the origin. Looking at the planet, each of them saw a silhouette of a man in the water. Was it possible that they saw the same man? Could he be Chapaev, who needed their help?

The first line contains two numbers separated with a space. The first number is the radius of the planet Ocean; it is an integer in the range from 1 to 1000. The second number is the refractive index of the planet Ocean; it is a real number in the range from 1 to 100 with at most two fractional digits. The second line contains Anka's coordinates and the coordinates of the vector along which she looks at the man in the water. The third line contains Petka's coordinates and the coordinates of the vector along which he looks at the man in the water. The numbers in the second and third lines are separated with a space; they are integers with absolute values not exceeding 1000. It is guaranteed that Petka and Anka are at distinct points outside the planet and the points they see are strictly inside the planet. Petka, Anka, and the men they see inside the planet Ocean must be regarded as points.

Output “Yes” if Petka and Anka may see the same man inside the planet and “No” otherwise. It is guaranteed that in the case of the answer “Yes” the man they see is at a distance of at least 10⁻⁴ from the boundary of the planet.

If α is the angle between an incident ray and the normal vector to the surface at the incidence point and β is the angle between the refracted ray and the normal vector to the surface, then the refractive index equals sin α / sin β.