**Problem : Double And Add One**

If you like numbers, you may have been fascinated by prime numbers.

Here's a problem related to prime numbers: Accept input numbers N and i. Identify all prime numbers P up to N with the following property:

P1=2*P+1 is also prime

P2=2*P1+1 is also prime

...

Pi=2*P(i-1)+1 is also prime

Example: Inputs N=100, i=3

Let's start with p=2(it is also prime ). Since i=3 we need 3 consecutive prime numbers that satisfy the Double and Add 1 property explained below:

p1=2*p+1 translates to p1=2*2+1=5, which is prime

p2=2*p1+1 translates to p2=2*5+1=11, which is prime

p3=2*p2+1 translates to p3=2*11+1=23, which is prime

Hence p=2 is to be included in the output.

Next, if p=3, the derived numbers are 7, 15, 31 of which 15 is not prime. Hence p=3 is not a solution

Exploring other primes up to 100 in this fashion, we identify the following additional numbers to be included in the solution for i=3:

5 (since the derived numbers 11, 23, 47 are all prime)

89 (since the derived numbers 179, 359, 719 are all prime)

Hence the output would be: 2, 5, 89

Input format for the example: 100 3

Output format for the example: 2 5 89

(Numbers separated by single space)

Here's a problem related to prime numbers: Accept input numbers N and i. Identify all prime numbers P up to N with the following property:

P1=2*P+1 is also prime

P2=2*P1+1 is also prime

...

Pi=2*P(i-1)+1 is also prime

Example: Inputs N=100, i=3

Let's start with p=2(it is also prime ). Since i=3 we need 3 consecutive prime numbers that satisfy the Double and Add 1 property explained below:

p1=2*p+1 translates to p1=2*2+1=5, which is prime

p2=2*p1+1 translates to p2=2*5+1=11, which is prime

p3=2*p2+1 translates to p3=2*11+1=23, which is prime

Hence p=2 is to be included in the output.

Next, if p=3, the derived numbers are 7, 15, 31 of which 15 is not prime. Hence p=3 is not a solution

Exploring other primes up to 100 in this fashion, we identify the following additional numbers to be included in the solution for i=3:

5 (since the derived numbers 11, 23, 47 are all prime)

89 (since the derived numbers 179, 359, 719 are all prime)

Hence the output would be: 2, 5, 89

Input format for the example: 100 3

Output format for the example: 2 5 89

(Numbers separated by single space)

**Input Format:**

First line contains an integer N

Second line contains integer i

**Output Format:**

Space delimited prime numbers satisfying Double and Add 1 property in the given range N

**Constraints:**

- 2< N <= 100000
- 1< i <= 10

**Sample Input and Output**

Example Number | Sample Input | Sample Output |
---|---|---|

1 | 100 3 | 2 5 89 |

2 | 20 2 | 2 5 11 |

If you have solved this program please help people to solve it by just commenting below in comment box..!!