Riemann Sum Offset (Small)

The integral of a function can be approximated like this.

$\int_a^b f(x)\,dx \approx \sum_{k=0}^{N-1} f(a + k\,\Delta x + \epsilon)\,\Delta x$

$\Delta x = \frac{b-a}{N}, \qquad 0 \le \epsilon \le \Delta x$

While working through integrals at boot camp, Mingyu wondered whether a well chosen $\epsilon$ could make this approximation match the true integral exactly. Checking that by hand runs into decimal arithmetic he cannot do on paper. Write the program that finds such an $\epsilon$ for him.

The first line contains a positive integer $K$, the degree of the polynomial. In this problem $K = 1$.

The second line contains the coefficients $c_1, c_2, \dots, c_{K+1}$ in decreasing order of degree. ($0 \le c_i \le 10$, $1 \le c_1 \le 10$)

The third line contains the integers $a$ and $b$, the start and the end of the integration interval, and $N$, the number of pieces the interval is split into. ($0 \le a < b \le 10$, $1 \le N \le 10$)

Print on one line the $\epsilon$ that makes the approximation equal the true integral. Round it to four decimal places and always print all four, so an answer of $0.25$ is printed as 0.2500.

If no such $\epsilon$ exists, print -1.

The integral of a power is computed like this.

$\int_a^b x^m\,dx = \frac{b^{m+1} - a^{m+1}}{m+1}$