Circle of Mistery

题号：NC256219
时间限制：C/C++/Rust/Pascal 1秒，其他语言2秒
空间限制：C/C++/Rust/Pascal 256 M，其他语言512 M
64bit IO Format: %lld

题目描述

Ran is good at solving graph problems, but this time she has a great trouble because the problem Yukari gives her is too hard! Ran needs your help!

So here's the Circle of Mistery Problem:

Give an integer array $w$ of length $n$ and an integer $k$ . Ran needs to construct a permutaion $p$ . Let's use $p$ to construct a graph: connect $i$ and $p_i$ together. Obviously, the graph will contain several circles. Ran has to make sure at least one circle $a_1\to a_2\to\dots\to a_x\to a_1$ ( $x\ge1$ ) satisfy that $\sum_{i=1}^x w_{a_i}\ge k$ . That means, circle $a_1\to a_1$ is legal.

Try to find the permutation $p$ with the minimum number of inversions and output the number. An inversion in an array $a$ is a pair of indices $(i, j)$ such that $i > j$ and $a_i < a_j$ .

输入描述:

The first line contains two integers  () and  ().
The next line contains  integers, the -th one means  ().

输出描述:

If it's impossible to construct , output . Otherwise output the minimum number of inversions in .

示例1

输入

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3 3
2 2 1

输出

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示例2

输入

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5 3
-3 2 -1 0 2

输出

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示例3

输入

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2 -3
-5 -5

输出

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-1

备注:

For the second sample, . The circle  satisfies the condition.