Segment Sum
A segment of a sequence a_1, a_2, …, a_N is a sequence a_i, a_{i+1}, …, a_j for some 1 ≤ i ≤ j ≤ N. Given an integer sequence consider a set of all its segments, ordered by the sum of elements. Your task is to find the sum of elements of K-th segment in this order (0-based). In this problem two segments are considered different, if one of their ends does not coincide. So actually it can be a multiset, for example for sequence 2, 2 all its different segments are {2}, {2}, {2,2}. Therefore any sequence of length N will have exactly N(N+1)/2 segments. For given example, their sums will be 2, 2, 4 in order.
Input
First line of input contains two integer numbers N and K – length of the sequence and 0-based number of interesting segment (1 ≤ N ≤ 10^5, 0 ≤ K < N(N+1)/2). Second line contains N integers a_1, a_2, …, a_N – the elements of the sequence (-10^9 ≤ a_i ≤ 10^9).
Output
Sum of elements of K-th segment in this order (0-based).