Similar statements (1) P70867

Consider two infinite horizontal lines A and B, separated ℓ units apart. The line A has m ‍points at the abscissae a₁, …, a_m. The line B has n points at the abscissae b₁, …, b_n. Given p ‍different indices i₁, …, i_p choosen from {1 … m}, and p different indices j₁, …, j_p choosen from {1 … n}, define d_k as the Euclidean distance between a_ik and b_jk, that is,

You are given ℓ, p, and the points in A and in B. Pick i₁, …, i_p and j₁, …, j_p in order to

Input

Input consists of several cases, each one with only integer numbers. Every case begins with four strictly positive numbers ℓ, p, m and n. Follow a₁ ≤ a₂ ≤ … ≤ a_m−1 ≤ a_m. Follow b₁ ≤ b₂ ≤ … ≤ b_n−1 ≤ b_n. Assume ℓ ≤ 10⁶, p ≤ min(m, n), and that the absolute value of each abscissa is at most 10⁶.

Additionally, assume that m and n are at most 1000.

Output

For every case, print the result with four digits after the decimal point. If you use the long double type, the input cases have no precision issues.