Given a floor of dimensions 2 x W and tiles of dimensions 2 x 1, the task is to find the number of ways the floor can be tiled. A tile can either be placed horizontally i.e as a 1 x 2 tile or vertically i.e as 2 x 1 tile. Print the answer modulo 109+7.
Input: W = 3 Output: 3 Explanation: We need 3 tiles to tile the board of size 2 x 3. We can tile in following ways: 1) Place all 3 tiles vertically. 2) Place first tile vertically. and remaining 2 tiles horizontally. 3) Place first 2 tiles horizontally and remaining tiles vertically.
Input: W = 4 Output: 5 Explanation: For a 2 x 4 board, there are 5 ways 1) All 4 vertical 2) All 4 horizontal 3) First 2 vertical, remaining 2 horizontal. 4) First 2 horizontal, remaining 2 vertical. 5) Corner 2 vertical, middle 2 horizontal.
You don't need to read input or print anything. Your task is to complete the function numberOfWays() which takes an Integer N as input and returns the answer.
Expected Time Complexity: O(N)
Expected Auxiliary Space: O(1)
1 <= N <= 105
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