how to find square root of an integer with binary search

gistfile1.java

public static int sqr(int a){
  
  if (a < 1) return 0;
  
  int low = 1;
  int h = a;
  
  
  while (low < h){
      
      int m = low + (h - low) / 2;
      
      int s = m * m;

      if (s == a){
          return m;
      } else if (s < a){
          low = m;
      } else {
          h = m;
      }
  }
  return 0;
}

This code is not properly updating the values. Will stuck in infinite loop. e.g. for a = 2.

This is the brilliant code in C++. For all n from 0 to 2^64 - 1.

#include <iostream>

unsigned long long binary_sqrt(uint64_t n) {
    __int128 left = 0, right = n, middle;

    if (n == 0) return 0;

    while (right - left > 1) {
        middle = (right + left) / 2;

        if (middle * middle <= n)
            left = middle;
        else
            right = middle;
    }

    return left;
}

int main() {
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(nullptr);

    uint64_t n;

    while (std::cin >> n)
        std::cout << binary_sqrt(n) << "\n";

    return 0;
}