Assistant System Engineer

You are given a string ‘S’ of length ‘N’. The string can be encoded using the following rules:

1) If the ‘i-th’ character is a vowel, change it to the next character in the alphabetical sequence. For example, the next character of ‘o’ is ‘p’.

2) If the ‘i-th’ character is a consonant, change it to the previous character in the alphabetical sequence. For example, the previous character of ‘h’ is ‘g’.

3) The next character of ‘z’ is ‘a’.

4) The previous character of ‘a’ is ‘z’.

Find the encoded string.

Example :

‘N’ = 4, ‘S’ = “code”

Character ‘c’ gets changed to ‘b’.
Character ‘o’ gets changed to ‘p’.
Character ‘d’ gets changed to ‘c’.
Character ‘e’ gets changed to ‘f’.

Encoded string = “bpcf”

You are given an array 'NUM' consisting of N positive Integers. Your task is to find the total number of possible sequences of positive integers (greater than 1) whose product is 'X'.

The value of 'X' is calculated as the product of the N terms, where the ith term is generated by raising the ith prime number to the power of an ith element in the given array.

In mathematical terms, we can write X as:

X = 2 ^ NUM[1] * 3 ^ NUM[2] * 5 ^ NUM[3] * 7 ^ NUM[4] * 11 ^ NUM[5] * … up to Nth term

Note :

1. Sum of all the elements in the array 'NUM' will always be less than or equal to 400.
2. As the total number of such sequences can be very large, print the answer modulo 1000000007.

You have given a sorted array 'A' of 'N' integers.

Now, you are given 'Q' queries, and each query consists of a single integer 'X'. Your task is to check whether 'X' is present in array 'A' or not for each query. If 'X' exists in array 'A', you need to print 1 else print 0.

Note :

The given array is sorted in non-decreasing order. 

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