Subsequence — Eolymp

Input

The first line contains two integers $n$ and $k$ ( $1 \leq n \leq 500000$ 1 \le n \le 500\,000, $- 1 0^{9} \leq k \leq 1 0^{9}$ -10^9 \le k \le 10^9) — the number of elements in the sequence and the desired sum.

The second line contains $n$ integers $a_{i}$ a_i ( $- 1 0^{9} \leq a_{i} \leq 1 0^{9}$ -10^9 \le a_i \le 10^9) — the elements of the sequence.

Output

Print one number $∣ k - l ∣$ |k - l| (the absolute difference between $k$ and $l$ ), where $l$ is the sum of the optimal segment of the sequence.

Examples

Example 1

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