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ZOJ Problem Set - 3868
GCD Expectation

Time Limit: 4 Seconds      Memory Limit: 262144 KB

Edward has a set of n integers {a1, a2,...,an}. He randomly picks a nonempty subset {x1, x2,…,xm} (each nonempty subset has equal probability to be picked), and would like to know the expectation of [gcd(x1, x2,…,xm)]k.

Note that gcd(x1, x2,…,xm) is the greatest common divisor of {x1, x2,…,xm}.


There are multiple test cases. The first line of input contains an integer T indicating the number of test cases. For each test case:

The first line contains two integers n, k (1 ≤ n, k ≤ 106). The second line contains n integers a1, a2,…,an (1 ≤ ai ≤ 106).

The sum of values max{ai} for all the test cases does not exceed 2000000.


For each case, if the expectation is E, output a single integer denotes E · (2n - 1) modulo 998244353.

Sample Input

5 1
1 2 3 4 5

Sample Output


Author: LIN, Xi
Source: The 15th Zhejiang University Programming Contest
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