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# Prime Time Problem

Prime Time Problem  is a simple coding problem which was asked in one of the sample problem of TCS CodeVita coding competition. TCS organizes this global level coding competition in order to promote Programming-As-a-Sport and in the search of world’s best Coder. This is the solution for the Codevita Question, Prime Time Problem.

## Problem Description

Here on earth, our 24-hour day is composed of two parts, each of 12hours. Each hour in each part has a corresponding hour in the other partseparated by 12 hours: the hour essentially measures the duration sincethe start of the day part. For example, 1 hour in the first part of the day is equivalent to 13, which is 1 hour into the second part of the day.Now, consider the equivalent hours that are both prime numbers.

We have 3 such instances for a 24-hour 2-part day:

• 5~17
• 7~19
• 11~23

Accept two natural numbers D, P >1 corresponding respectively to numberof hours per day and number of parts in a day separated by a space. D should be divisible by P, meaning that the number of hours per part (D/P) should be a natural number. Calculate the number of instances of equivalent prime hours. Output zero if there is no such instance.

Note – That we require each equivalent hour in each part in a day to be a prime number.

Example:

Input:

• 24 2

Output:

• 3 (We have 3 instances of equivalent prime hours: 5~17, 7~19 and 11~23.)

Constraints:

• 10 <= D < 500
• 2 <= P < 50

Input:

• Single line consists of two space separated integers, D and P corresponding to number of hours per day and number of parts in a day respectively.

Output:

• Output must be a single number, corresponding to the number of instances of equivalent prime number, as described above

Time Limit:

• 1

Examples

Example 1

Input

36 3

Output

2

Explanation

In the given test case D = 36 and P = 3

Duration of each day part = 12

2~14~X

3~15~X

5~17~29 – instance of equivalent prime hours

7~19~31 – instance of equivalent prime hours

11~23~X

Example 2

Input

49 7

Output

0

Explanation

Duration of each day part = 7

2~9~X~23~X~37~X

3~X~17~X~31~X~X

5~X~19~X~X~X~47

7~X~X~X~X~X~X

Hence there are no equivalent prime hours.

## Solution for Prime Time Problem

`#  To check prime you do not need run the loop till N, rather SQRT(N)import mathdef prime(n):    if n == 1:        return False    for i in range(2, int(math.sqrt(n) + 1)):        if n % i == 0:            return False    return Trued, p = map(int, (input().split()))n = int(d / p)count = 0# as 0, 1 not prime so starting from 2for i in range(2, n):    prime_time = True    for j in range(p):        num = i + j*n        if not prime(num):            prime_time = False            break    if prime_time:        count += 1print(count)`
`import mathn = 505prime_list = [True for i in range(n + 1)]pr = 2# Sieve of Eratostheneswhile pr * pr <= n:    if prime_list[pr] == True:        for i in range(pr * 2, n + 1, pr):            prime_list[i] = False    pr += 1prime_list[0] = Falseprime_list[1] = Falsed, p = map(int, (input().split()))n = int(d / p)count = 0# as 0, 1 not prime so starting from 2for i in range(2, n):    prime_time = True    for j in range(p):        num = i + j * n        if not prime_list[num]:            prime_time = False            break    if prime_time:        count += 1print(count)`