largest smaller or equal value

private int (int[] arr, int target) {
  if (arr == null || arr.length == 0) {
      return -1;
  }
  int start = 0, end = arr.length - 1;
  while (start + 1 < end) {
    int mid = start + (end - start) / 2;
    if (arr[mid] <= target) {
      start = mid;
    } else {
      end = mid;
    }
  }
  
  if (arr[end] <= target) {
    return end;
  } else if (arr[start] <= target) {
    return start;
  }
  return -1;

}