Subsequence

A sequence a[n] of integers consists of n elements. For a given number k find a non-empty subsequence a[i], a[i+1], ... a[i+m] of consecutive elements of the sequence a[n], such that the sum of its elements as close as possible to k.

Input

The first line contains two integers n and k (1 ≤ n ≤ 500000, -10^9 ≤ k ≤ 10^9) - number of elements in the sequence and the desired sum. The second line is followed by n integers a[i] (-10^9 ≤ a[i] ≤ 10^9) - the elements of the sequence.

Output

Print one number |k – l| (absolute difference of k – l), where l is the total sum on optimum segment of the sequence.

Examples