#include <bits/stdc++.h> 

int binarySearch(long long int N,int start,int end, int& num){

    

    long long int mid = start + (end-start)/2;
    //cout<<"Start: "<<start << " End: " <<  end<<" Mid: "<<mid<<endl;
    long long int square = mid*mid;
    if(start>end){
        return num;
    }
    
    if(square<=N){
        num = mid;
        start = mid+1;
    }else{
        end = mid-1;
    }

    binarySearch(N,start,end,num);

    return num;

}

int sqrtN(long long int N)
{
    int start = 0;
    int end = N;

    int sqrt = 0;

    binarySearch(N, start, end, sqrt);

    return sqrt;
}

我正在写一个用递归二进制搜索求平方根的代码。在我的这个代码中，它对于非常大的数字是失败的，有人能帮助我解决这个问题吗