Water Tank

A water tank with capacity $C$ liters is empty. At time 0 water starts flowing in through a pipe. The inflow is divided into $n$ consecutive phases numbered 0 to $n-1$. Phase $i$ lasts $t[i]$ seconds, and during that phase the tank receives $x[i]$ liters per second.

The tank has one outlet with a valve. The valve releases $R$ liters per second, where $R$ is a real number that is at least 0. You set $R$ before the water starts flowing and cannot change it until the inflow ends. While the tank is empty nothing drains out, so the stored amount never drops below 0.

Find the smallest $R$ for which the stored amount never exceeds $C$ liters at any moment.

The first line contains $n$ and $C$. ($1 \le n \le 50$, $1 \le C \le 10^9$)

The second line contains $t[0], t[1], \dots, t[n-1]$, and the third line contains $x[0], x[1], \dots, x[n-1]$. ($1 \le t[i], x[i] \le 10^6$)

Print the smallest $R$ on the first line as an irreducible fraction $p/q$. Here $p$ and $q$ are integers with $q \ge 1$ and $\gcd(p, q) = 1$. Print the denominator even when the answer is an integer or 0. An answer of 0 is printed as 0/1, and an answer of 2 is printed as 2/1.