You have a **1-indexed** binary string of length `n` where all the bits are `0` initially. We will flip all the bits of this binary string (i.e., change them from `0` to `1`) one by one. You are given a **1-indexed** integer array `flips` where `flips[i]` indicates that the bit at index `i` will be flipped in the `ith` step.

A binary string is **prefix-aligned** if, after the `ith` step, all the bits in the **inclusive** range `[1, i]` are ones and all the other bits are zeros.

Return _the number of times the binary string is **prefix-aligned** during the flipping process_.

**Example 1:**

**Input:** flips = \[3,2,4,1,5\]
**Output:** 2
**Explanation:** The binary string is initially  "00000 ".
After applying step 1: The string becomes  "00100 ", which is not prefix-aligned.
After applying step 2: The string becomes  "01100 ", which is not prefix-aligned.
After applying step 3: The string becomes  "01110 ", which is not prefix-aligned.
After applying step 4: The string becomes  "11110 ", which is prefix-aligned.
After applying step 5: The string becomes  "11111 ", which is prefix-aligned.
We can see that the string was prefix-aligned 2 times, so we return 2.

**Example 2:**

**Input:** flips = \[4,1,2,3\]
**Output:** 1
**Explanation:** The binary string is initially  "0000 ".
After applying step 1: The string becomes  "0001 ", which is not prefix-aligned.
After applying step 2: The string becomes  "1001 ", which is not prefix-aligned.
After applying step 3: The string becomes  "1101 ", which is not prefix-aligned.
After applying step 4: The string becomes  "1111 ", which is prefix-aligned.
We can see that the string was prefix-aligned 1 time, so we return 1.

**Constraints:**

*   `n == flips.length`
*   `1 <= n <= 5 * 104`
*   `flips` is a permutation of the integers in the range `[1, n]`.


def find_kth_palindrome(k, int_length):
    mid = (int_length + 1) // 2
    limit = 10 ** mid - 1

    i = 0
    while i <= limit:
        num = str(i)
        rev = num[::-1]
        if int_length % 2 != 0:
            rev = rev[1:]
        palindrome = int(num + rev)
        if palindrome > 0:
            k -= 1
        if k == 0:
            return palindrome
        i += 1
    return -1


def palindrome_queries(queries, int_length):
    return [find_kth_palindrome(query, int_length) for query in queries]
