SOLVE

LATER

GCD problem

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For each set of four integers given \((i,j ,k,l)\) where \(1\leq i < j <k <l \leq N\). You are required to compute the following:

\(\displaystyle\sum_{i=1}^{N} \displaystyle\sum_{j=i+1}^{N}\displaystyle\sum_{k=j+1}^{N} \displaystyle\sum_{l=k+1}^{N} gcd(i,j,k,l) ^{4}\)

**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
\(1 \leq T \leq 10 \\ 1 \leq N \leq 10^5\)**

Explanation

**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**

Time Limit:
5.0 sec(s)
for each input file.

Memory Limit:
256 MB

Source Limit:
1024 KB

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