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)