Problem: Check if a king can move a valid move or not when N nights are there in a modified chessboard
Given an infinite chessboard with the same rules as that of chess. Also given are N knights coordinates on the infinite chessboard(-10^9 <= x, y <= 10^9) and the king's coordinate, the task is to check if the King is checkmate or not.

Sample Input: a[] = { {1, 1} } king -> {3, 4}
Sample Output: No
The king can make valid moves.

Solution (python3):
# Python3 program for checking if a king 
# can move a valid move or not when 
# N nights are there in a modified chessboard 

def checkCheckMate(a, n, kx, ky): 

    # Pair of hash to mark the coordinates 
    mpp = {} 

    # iterate for Given N knights 
    for i in range(0, n): 
        x = a[i][0] 
        y = a[i][1] 

        # mark all the "L" shaped coordinates 
        # that can be reached by a Knight 

        # initial position 
        mpp[(x, y)] = 1

        # 1-st move 
        mpp[(x - 2, y + 1)] = 1

        # 2-nd move 
        mpp[(x - 2, y - 1)] = 1

        # 3-rd move 
        mpp[(x + 1, y + 2)] = 1

        # 4-th move 
        mpp[(x + 1, y - 2)] = 1

        # 5-th move 
        mpp[(x - 1, y + 2)] = 1

        # 6-th move 
        mpp[(x + 2, y + 1)] = 1

        # 7-th move 
        mpp[(x + 2, y - 1)] = 1

        # 8-th move 
        mpp[(x - 1, y - 2)] = 1
    
    # iterate for all possible 8 coordinates 
    for i in range(-1, 2): 
        for j in range(-1, 2): 
            nx = kx + i 
            ny = ky + j 
            
            if i != 0 and j != 0: 
                
                # check a move can be made or not 
                if not mpp[(nx, ny)]: 
                    return True
    
    # any moves 
    return False

# Driver Code 
if __name__ == "__main__": 

    a = [[1, 0], [0, 2], [2, 5], 
         [4, 4], [5, 0], [6, 2]] 

    n = len(a) 
    x, y = 3, 2
    
    if checkCheckMate(a, n, x, y): 
        print("Not Checkmate!") 
    else:
        print("Yes its checkmate!")