Can you solve this keygen problem?

[UniSoft]

Originally Posted by dila

The objective is to find valid 64-bit input keys that make the function return 'true'.

1. How many valid input keys are there?

A lot...

#include <stdlib.h>
#include <stdio.h>
#include <stdint.h>
#include <stdbool.h>
#include <time.h>

bool check_key(uint64_t x) {
  uint64_t r = x;
  for (size_t i = 0; i < 64; ++i) {
    for (size_t j = 0; j < 6; ++j) {
      r ^= (((x >> (1 << j)) & (i >> j) & 1) << i);
    }
  }
  return (x && r == 0);
}

uint64_t generate(void) {
  uint64_t r, x;

  do {
    x = (((uint64_t)rand() * rand()) * rand()) ^ rand();
    r = 0;
    for (size_t i = 0; i < 64; ++i) {
      for (size_t j = 0; j < 6; ++j) {
        r ^= (((x >> (1 << j)) & (i >> j) & 1) << i);
      }
    }
  } while (r == 0);
  return r;
}

int main(int argc, char *argv[])
{
    uint64_t r;
    srand((unsigned)time(NULL));

    r = generate();
    if (check_key(r))
        printf("%016llu => OK\n", r);
    else
        printf("%016llu => FAIL\n", r);

    //_getch();
    return 0;
}