C++ reverse with for

Question

Hey in one of the exercises I can't seem to find my mistake. (I know there is a reverse function but id like to understand why I can't fill strings like this

#include <iostream>
#include <string>
using namespace std;

bool isPalindrome(int x) {
//complete the function

string a=to_string(x);
string b;
for(long int i=a.length();i>=a.length()-1;i--){
b[a.length()-i]=a[i];

}
if(b==a){return true;}
else{return false;}
}

int main() {
int n;
cin >>n;

if(isPalindrome(n)) {
cout <<n<<" is a palindrome";
}
else {
cout << n<<" is NOT a palindrome";
}
return 0;
}

Answer 1

string a = to_string(x);
string b;
for(long int i=a.length();i!=0;i--){
b.push_back(a[i-1]);

}