Remainder
Description
You are given a huge decimal number consisting of $n$ digits. It is guaranteed that this number has no leading zeros. Each digit of this number is either 0 or 1.
You may perform several (possibly zero) operations with this number. During each operation you are allowed to change any digit of your number; you may change 0 to 1 or 1 to 0. It is possible that after some operation you can obtain a number with leading zeroes, but it does not matter for this problem.
You are also given two integers $0 \le y < x < n$. Your task is to calculate the minimum number of operations you should perform to obtain the number that has remainder $10^y$ modulo $10^x$. In other words, the obtained number should have remainder $10^y$ when divided by $10^x$.
The first line of the input contains three integers $n, x, y$ ($0 \le y < x < n \le 2 \cdot 10^5$) — the length of the number and the integers $x$ and $y$, respectively.
The second line of the input contains one decimal number consisting of $n$ digits, each digit of this number is either 0 or 1. It is guaranteed that the first digit of the number is 1.
Print one integer — the minimum number of operations you should perform to obtain the number having remainder $10^y$ modulo $10^x$. In other words, the obtained number should have remainder $10^y$ when divided by $10^x$.
Input
The first line of the input contains three integers $n, x, y$ ($0 \le y < x < n \le 2 \cdot 10^5$) — the length of the number and the integers $x$ and $y$, respectively.
The second line of the input contains one decimal number consisting of $n$ digits, each digit of this number is either 0 or 1. It is guaranteed that the first digit of the number is 1.
Output
Print one integer — the minimum number of operations you should perform to obtain the number having remainder $10^y$ modulo $10^x$. In other words, the obtained number should have remainder $10^y$ when divided by $10^x$.
Samples
11 5 2
11010100101
1
11 5 1
11010100101
3
Note
In the first example the number will be $11010100100$ after performing one operation. It has remainder $100$ modulo $100000$.
In the second example the number will be $11010100010$ after performing three operations. It has remainder $10$ modulo $100000$.