string cipher(int k, string s) {
    int n = s.size();
    string res = "";
    res.push_back(s[0]);
    
    for(int i=1;i<n-k+1;i++){
        if(i < k){
            int x = (int)(s[i]-'0') ^ (int)(s[i-1]-'0');
            char ch = ('0'+x);
            res.push_back(ch);
        }
        else{
            int r = res.size();
            int x = 0;
            for(int j=r-1;j>=r-k+1;j--){
                x ^= (int)(res[j]-'0');
            }
            x ^= (int)(s[i]-'0');
            char ch = (char)('0'+x);
            res.push_back(ch);
        }
    }
    return res;
}