Faithful Numbers
Easy Accuracy: 47.41% Submissions: 268 Points: 2

A number is called faithful if you can write it as the sum of distinct powers of 7. 
e.g.,  2457 = 7 + 72 + 74 . If we order all the faithful numbers, we get the sequence 1 = 70, 7 = 71, 8 = 70 + 71, 49 = 72, 50 = 70 + 72 . . . and so on.
Given some value of N, you have to find the N'th faithful number.

 

Example 1:

Input:
N = 3
Output:
8
Explanation:
8 is the 3rd Faithful number.

Example 2:

Input:
N = 7
Output:
57
Explanation:
57 is the 7th Faithful number.

 

Your Task:
You don't need to read input or print anything. Your task is to complete the function nthFaithfulNum() which takes an Integer N as input and returns the answer.

 

Expected Time Complexity: O(log(N))
Expected Auxiliary Space: O(log(N))

 

Constraints:
1 <= N <= 105

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