403755: GYM101257 G 24

Round 16,777,216 of Codeforce-is has just finished, and all the contestants were able to pass the pretests in problem A.

Maike, the founder of Codeforce-is wants to measure how weak the tests for problem A were, so he became interested in finding the amount of changes that will occur on the contest’s scoreboard after the system tests.

Given the score for problem A, the score of each contestant before the system tests, and the probability of failing the system tests for each contestant’s solution, can you help Maike find the expected number of pairs of contestants that will swap their relative order after the system tests? That is, the number of pairs of contestants i, j such that the score_i  >  score_j before the system tests, but score_i  <  score_j after the system tests.

The first line of input consists of two integers, N (2 ≤ N ≤ 10⁵), and S_A (1 ≤ S_A ≤ 10⁵), the number of contestants in the round, and the score the contestants achieved for passing the pretests of problem A.

The second line contains N space-separated integers, the K^th integer is T_K (S_A ≤ T_K ≤ 10⁵) which represents the total score in the contest for the K^th contestant before the system tests, T_i  ≥  T_i + 1 for (1 ≤ i < N).

The third and final line contains N space-separated numbers, the K^th number is P_K (0.01 ≤ P_K ≤ 1.00) which represents the probability that the K^th contestant's solution will fail the system tests. Numbers are given with exactly two digits after the decimal point.

On a single line, output the expected number of pairs of contestants that will swap their relative order after the system tests are over.

2 10
25 20
0.50 0.50

0.250000000

4 10
25 20 15 15
1.00 0.50 1.00 0.50

0.750000000