CF1165A Remainder

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 $ .

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 $ .