I-Identical Day_上海理工大学第二届“联想杯”全国程序设计邀请赛

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

Kyon realizes he's experiencing identical days over and over again. The only difference between them is the appearance of Suzumiya Haruhi.

When Haruhi appears, Kyon will mark the day with $0$ . And if she doesn't, Kyon will mark the day with $1$ .

One day, Kyon suddenly has the ability to make Haruhi appear. In other words, he can change $1$ to $0$ as many times as he likes. And he defines the UNHAPPY of $l$ continuous day without Haruhi as $\frac{l\times (l+1)}{2}$ .

For example, the total UNHAPPY of $0111101$ equals to $\frac{4\times 5}{2}+\frac{1\times 2}{2}=10+1=11$ .

Now Kyon wants to know the minimum times he must make Haruhi appear so that the total UNHAPPY of $n$ days is no more than $k$ .

输入描述:

The first line contains two integer $n,k(1 \leq n \leq 10^5,0 \leq k \leq 10^{10})$ .

The second line contains a string $s$ . Each character of the string $s$ is either $1$ or $0$ and the length of $s$ is $n$ .

输出描述:

Output one integer indicating the answer.

示例1

输入

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7 4
1110111

输出

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示例2

输入

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3 1
111

输出

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