B. Make Almost Equal With Mod

time limit per test

1 second

memory limit per test

256 megabytes

⠀

You are given an array a1,a2,...,an of distinct positive integers. You have to do the following operation exactly once:

choose a positive integer k;
for each i from 1 to n, replace ai with ai mod k†.

Find a value of k such that 1≤k≤1018 and the array a1,a2,...,an contains exactly 2 distinct values at the end of the operation. It can be shown that, under the constraints of the problem, at least one such k always exists. If there are multiple solutions, you can print any of them.

† a mod b denotes the remainder after dividing a by b. For example:

7 mod 3=1 since 7=3⋅2+1
15 mod 4=3 since 15=4⋅3+3
21 mod 1=0 since 21=21⋅1+0

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1≤t≤500). The description of the test cases follows.

The first line of each test case contains a single integer n (2≤n≤100) --- the length of the array a.

The second line of each test case contains n integers a1,a2,...,an (1≤ai≤1017) --- the initial state of the array. It is guaranteed that all the ai are distinct.

Note that there are no constraints on the sum of n over all test cases.

Output

For each test case, output a single integer: a value of k (1≤k≤1018) such that the array a1,a2,...,an contains exactly 2 distinct values at the end of the operation.

Example

Input

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8 15 22 30

60 90 98 120 308

328 769 541 986 215 734

1000 2000 7000 11000 16000

2 1

Output

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7
30
3
5000
1000000000000000000

Note

In the first test case, you can choose k=7. The array becomes $8 mod 7,15 mod 7,22 mod 7,30 mod 7$ = $1,1,1,2$ , which contains exactly 2 distinct values ({1,2}).

In the second test case, you can choose k=30. The array becomes $0,0,8,0,8$ , which contains exactly 2 distinct values ({0,8}). Note that choosing k=10 would also be a valid solution.

In the last test case, you can choose k=1018. The array becomes $2,1$ , which contains exactly 2 distinct values ({1,2}). Note that choosing k=1018+1 would not be valid, because 1≤k≤1018 must be true.

解题说明：此题是一道数学题，选择一个正整数k，将数组每个元素变为a(i)%k ，求解k设为什么值可以使得原数组有且仅有两种值。找规律能发现只需要找到所有元素相对于第一个元素的偏移量的最大公约数，然后乘以2就是需要的值。

cpp 复制代码

#include<bits/stdc++.h>
#include<iostream>
#include<cmath>
#include<algorithm>
using namespace std;
int main() 
{
    long long int t, n; 
    cin >> t;
    while (t-- && cin >> n) 
    {
        long long int a[n], k = 0; 
        for (int i = 0; i < n; i++)
        {
            cin >> a[i];
            k = __gcd(k, abs(a[i] - a[0]));
        }
        cout << k + k << '\n';
    }
    return 0;
}