Number Theory Problem (Prime Number Problem)

Number Theory Problem (Prime Number Problem)

Problem:

A certain strange mathematician, Rasyak, considers a particular set of prime numbers beautiful. He also calls a composite number beautiful, if it is divisible by at least one prime number in his chosen set of beautiful primes. Given Rasyak’s set of M beautiful primes and an integer N, you have to find the number of beautiful numbers (both primes and composites) between 1 and N. For example, given a set of 2 beautiful primes, {2, 5}, there are 6 beautiful numbers between 1 and 10 (i.e. 2, 4, 5, 6, 8 and 10).

Input

The first line of the input gives the number of test cases, T (1 <= T <= 100). T test cases follow. Each will consist of one line containing a single integer M, followed by a line containing M space-separated prime numbers mi, followed by another line containing a single integer N.

1 <= M <= 25

1 <= mi <= 1000

1 <= N <= 2*10^9

Output

For each test case, output one line containing a single integer X, where X is the number of beautiful numbers between 1 and N.

Input

2
2 5
10

3
2 5 13
100

25
2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97
2000000000

Output

1759360857

How can i solve this problem???

any idea????