A gas station too far

There is just one road connecting the $n+1$ cities $c_0, \dots, c_n$ consecutively. You want to go from $c_0$ to $c_n$ stopping at most $s$ times to fill the tank of the car. There are gas stations at the cities, but none on the roads. The length of each road is $\ell_0, \dots, \ell_{n-1}$ . Which is the minimum range for your car? Suppose that you start with a full tank.

Input

Input consists of several cases. Every case begins with $n$ and $s$ , which are followed by $n$ natural numbers $\ell_0, \dots, \ell_{n-1}$ . Suppose $1 \le n \le 10^5$ , $0 \le s \le n - 1$ , and $1 \le \ell_i \le 10^4$ .

Output

For every case, print the minimum range for a car to reach $c_n$ starting from $c_0$ stopping at most $s$ times to fill the tank.

Hint

Consider a decisional version of this problem.

Problem information

Author: Unknown
Translator: Salvador Roura

Generation: 2026-01-25T10:18:51.759Z