Project Engineer

You are given a positive integer ‘N’. Your task is to print all prime numbers less than or equal to N.

Note: A prime number is a natural number that is divisible only by 1 and itself. Example - 2, 3, 17, etc.

You can assume that the value of N will always be greater than 1. So, the answer will always exist.

Ninja has a binary string ‘S’ of length ‘N’. Initially, all the characters in a string are ‘1’, i.e.

S[i] = ‘1’ for each 1 <= ‘i’ <= ‘N’.

An operation is defined as choosing a number between 1 to 4, and doing the following steps accordingly.

1. If the chosen number is 1, then flip all the characters in string.

2. If the chosen number is 2, then flip all the characters at odd indexes.

3. If the chosen number is 3, then flip all the characters at even indexes.

4. If the chosen number is 4, then flip all the characters at (3k + 1) indexes. 

You need to find out that after performing operations exactly ‘M’ number of times, how many distinct final strings can be there.

Note :

1. A binary string is a string in which all characters are either ‘1’ or ‘0’.

2. Flipping a character means that if the character is ‘1’ then change it to 0, or if it is ‘0’ then change it to ‘1’.

Normalisation

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