Haru Dermatology

In 2023, Haru opened a dermatology clinic and treats acne with HARU-LASER, a laser made for acne.

The shape of an acne spot is given by the quadratic $f(x) = ax^2+bx+c$. The laser is set to the linear function $g(x) = dx+e$, and its intensity is defined as $\int_{x_1}^{x_2} \{f(x) - g(x)\}\,\mathrm{d}x$.

Here $x_1$ and $x_2$ are the x-coordinates of the two ends of the acne. The domains of $f(x)$ and $g(x)$ are $(-\infty, \infty)$.

Haru opened the clinic not long ago and still struggles to calculate the laser intensity. Calculate it for Haru.

The first line contains $x_1$ and $x_2$ separated by a space.

The second line contains the coefficients $a$, $b$, $c$, $d$, and $e$ separated by spaces.

All input numbers are integers. The input is guaranteed to give a laser intensity that is an integer with absolute value at most $10^{9}$.

Print the laser intensity on the first line.

• $-30 \leq x_1 < x_2 \leq 30$
• $-30 \leq a,b,c,d,e \leq 30$
• $a,d \neq 0$
• $a$ is a multiple of $3$
• $b$ and $d$ are multiples of $2$