kth-digit-string.cpp

ll kth_digit_string(ll k) {
  if (k < 10) return k;

  ll c = 180, i = 2, u = 10, r = 0, ans = -1, m;
  for (k -= 9; k > c; i++, u *= 10) {
    k -= c;
    c /= i;
    c *= 10 * (i + 1);
  }

  if ((m = k % i))
    r++;
  else
    m = i;

  ll tmp = (k / i) + r + u - 1;
  for (m = i + 1 - m; m--; tmp /= 10) ans = tmp % 10;

  return ans;
}