A coding problem. The trick is, some part of computation can be reused from last iteration. Check out my code:

#include <cmath>
#include <cstdio>
#include <vector>
#include <bitset>
#include <map>
#include <set>
#include <string>
#include <iostream>
#include <algorithm>
using namespace std;

#define MAX_CNT 2000002

int main() 
{
    int n, k;
    cin >> n >> k;
    
    std::bitset<MAX_CNT> b;
    string in; getline(cin, in); getline(cin, in);
    size_t len = in.length();
    for (int i = 0; i < len; i++)
        b[i] = in[len - i - 1] - '0';

    std::bitset<MAX_CNT> r;
    string rs;
    unsigned char lstXor = 0;
    for (int i = 0; i < n; i++)
    {
        size_t cnt = std::min(k - 1, i);
        unsigned char c = b[i];
        
        if (i > 0) lstXor ^= r[i - 1];
        if (i >= k) lstXor ^= r[i - k];
        r[i] = c ^ lstXor;
        
        rs += r[i] ? '1' : '0';
    }
    std::reverse(rs.begin(), rs.end());
    cout << rs << endl;

    return 0;
}