The **numeric value** of a **lowercase character** is defined as its position `(1-indexed)` in the alphabet, so the numeric value of `a` is `1`, the numeric value of `b` is `2`, the numeric value of `c` is `3`, and so on.

The **numeric value** of a **string** consisting of lowercase characters is defined as the sum of its characters' numeric values. For example, the numeric value of the string `"abe "` is equal to `1 + 2 + 5 = 8`.

You are given two integers `n` and `k`. Return _the **lexicographically smallest string** with **length** equal to `n` and **numeric value** equal to `k`._

Note that a string `x` is lexicographically smaller than string `y` if `x` comes before `y` in dictionary order, that is, either `x` is a prefix of `y`, or if `i` is the first position such that `x[i] != y[i]`, then `x[i]` comes before `y[i]` in alphabetic order.

**Example 1:**

**Input:** n = 3, k = 27
**Output:**  "aay "
**Explanation:** The numeric value of the string is 1 + 1 + 25 = 27, and it is the smallest string with such a value and length equal to 3.

**Example 2:**

**Input:** n = 5, k = 73
**Output:**  "aaszz "

**Constraints:**

*   `1 <= n <= 105`
*   `n <= k <= 26 * n`


def contains_cycle(grid):
    def dfs(x, y, start_x, start_y, depth):
        if x < 0 or y < 0 or x >= len(grid) or y >= len(grid[0]) or grid[x][y] != grid[start_x][start_y]:
            return False

        grid[x][y] = '*'

        directions = [(0, 1), (0, -1), (1, 0), (-1, 0)]
        for dx, dy in directions:
            new_x, new_y = x + dx, y + dy

            if new_x == start_x and new_y == start_y and depth >= 4:
                return True

            if dfs(new_x, new_y, start_x, start_y, depth + 1):
                return True

        grid[x][y] = grid[start_x][start_y]

        return False

    for i in range(len(grid)):
        for j in range(len(grid[0])):
            if dfs(i, j, i, j, 0):
                return True

    return False
