```python
def minPath(grid, k):
    """
    Given a grid with N rows and N columns (N >= 2) and a positive integer k, 
    each cell of the grid contains a value. Every integer in the range [1, N * N]
    inclusive appears exactly once on the cells of the grid.

    You have to find the minimum path of length k in the grid. You can start
    from any cell, and in each step you can move to any of the neighbor cells,
    in other words, you can go to cells which share an edge with you current
    cell.
    Please note that a path of length k means visiting exactly k cells (not
    necessarily distinct).
    You CANNOT go off the grid.
    A path A (of length k) is considered less than a path B (of length k) if
    after making the ordered lists of the values on the cells that A and B go
    through (let's call them lst_A and lst_B), lst_A is lexicographically less
    than lst_B, in other words, there exist an integer index i (1 <= i <= k)
    such that lst_A[i] < lst_B[i] and for any j (1 <= j < i) we have
    lst_A[j] = lst_B[j].
    It is guaranteed that the answer is unique.
    Return an ordered list of the values on the cells that the minimum path go through.

    Examples:

        Input: grid = [ [1,2,3], [4,5,6], [7,8,9]], k = 3
        Output: [1, 2, 1]

        Input: grid = [ [5,9,3], [4,1,6], [7,8,2]], k = 1
        Output: [1]
    """
    n = len(grid)
    
    # Find the position of value 1, since the lexicographically smallest path
    # must start with the smallest possible value, which is 1.
    # Actually, we need to find the minimum path of length k.
    # The first element of the path should be as small as possible.
    # So we start from the cell containing 1.
    
    # Find position of 1
    pos1 = None
    for i in range(n):
        for j in range(n):
            if grid[i][j] == 1:
                pos1 = (i, j)
                break
        if pos1:
            break
    
    # Directions: up, down, left, right
    directions = [(-1, 0), (1, 0), (0, -1), (0, 1)]
    
    # We need to find the lexicographically smallest path of length k starting from 1.
    # Since we want lexicographically smallest, at each step we should choose the neighbor
    # with the smallest value. But we need to be careful: the path is a sequence of values.
    # Starting from 1, at each step, among all neighbors, we pick the one with the smallest value.
    # This greedy approach works because lexicographic order prioritizes earlier positions.
    
    path = [1]
    current = pos1
    
    for _ in range(k - 1):
        # Find all neighbors of current cell
        neighbors = []
        for di, dj in directions:
            ni, nj = current[0] + di, current[1] + dj
            if 0 <= ni < n and 0 <= nj < n:
                neighbors.append((grid[ni][nj], (ni, nj)))
        
        # Pick the neighbor with the smallest value
        min_val, min_pos = min(neighbors)
        path.append(min_val)
        current = min_pos
    
    return path
```