Your task is to evaluate the following definite integral:
where P(x) = a4 · x4 + a3 · x3 + a2 · x2 + a1 · x + a0. P(x) has no real roots and GCD(P(x), P'(x)) = const.
The input contains five integers: a0, a1, a2, a3 and a4 separated by whitespace. Each of these numbers does not exceed 106 by absolute value, a4 ≠ 0.
Output the value of the integral. Assume that the exact value is A
and your answer is B
. Your answer will be considered correct if and only if at least one of the following statements is true:
- A − 10−9 ≤ B ≤ A + 10−9
- A · (1 − 10−9) ≤ B ≤ A · (1 + 10−9)
16 0 0 0 1
Problem Source: SPbSU ITMO contest. Petrozavodsk training camp. Winter 2008.