For each set of four integers given \((i,j ,k,l)\) where \(1\leq i < j
\(\displaystyle\sum_{i=1}^{N} \displaystyle\sum_{j=i+1}^{N}\displaystyle\sum_{k=j+1}^{N} \displaystyle\sum_{l=k+1}^{N} gcd(i,j,k,l) ^{4}\)
Input format
- First line: \(T\) that denotes the number of test cases
- Next \(T\) lines: A integer \(N\)
Output format
Print the answer for each test case \(Mod \,\,\,10^9+7\) in a new line.
Constraints
For First Test case N=4 :
(1,2,3,4) : gcd(1,2,3,4)4 = 1
Total sum = 1
For Second Test Case N=5 :
(1,2,3,4) : gcd(1,2,3,4)4 = 1
(1,2,3,5) : gcd(1,2,3,5)4 = 1
(1,2,4,5) : gcd(1,2,4,5)4 = 1
(1,3,4,5) : gcd(1,3,4,5)4 = 1
(2,3,4,5) : gcd(2,3,4,5)4 = 1
Total sum = 1+1+1+1+1 = 5
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