E. Best Pairtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputYou are given an array a of length n. Let cnt_x be the number of elements from the array which are equal to x. Let's also define f(x, y) as (cnt_x + cnt_y) \cdot (x + y).Also you are given m bad pairs (x_i, y_i). Note that if (x, y) is a bad pair, then (y, x) is also bad.Your task is to find the maximum value of f(u, v) over all pairs (u, v), such that u \neq v, that this pair is not bad, and also that u and v each occur in the array a. It is guaranteed that such a pair exists.InputThe first line contains a single integer t (1 \le t \le 10\,000) — the number of test cases.The first line of each test case contains two integers n and m (2 \le n \le 3 \cdot 10^5, 0 \le m \le 3 \cdot 10^5) — the length of the array and the number of bad pairs.The second line of each test case contains n integers a_1, a_2, \ldots, a_n (1 \le a_i \le 10^9) — elements of the array.The i-th of the next m lines contains two integers x_i and y_i (1 \le x_i < y_i \le 10^9), which represent a bad pair. It is guaranteed that no bad pair occurs twice in the input. It is also guaranteed that cnt_{x_i} > 0 and cnt_{y_i} > 0.It is guaranteed that for each test case there is a pair of integers (u, v), u \ne v, that is not bad, and such that both of these numbers occur in a.It is guaranteed that the total sum of n and the total sum of m don't exceed 3 \cdot 10^5.OutputFor each test case print a single integer — the answer to the problem.ExampleInput
3
6 1
6 3 6 7 3 3
3 6
2 0
3 4
7 4
1 2 2 3 1 5 1
1 5
3 5
1 3
2 5
Output
40
14
15
NoteIn the first test case 3, 6, 7 occur in the array.   f(3, 6) = (cnt_3 + cnt_6) \cdot (3 + 6) = (3 + 2) \cdot (3 + 6) = 45. But (3, 6) is bad so we ignore it.  f(3, 7) = (cnt_3 + cnt_7) \cdot (3 + 7) = (3 + 1) \cdot (3 + 7) = 40.  f(6, 7) = (cnt_6 + cnt_7) \cdot (6 + 7) = (2 + 1) \cdot (6 + 7) = 39. The answer to the problem is \max(40, 39) = 40.
3
6 1
6 3 6 7 3 3
3 6
2 0
3 4
7 4
1 2 2 3 1 5 1
1 5
3 5
1 3
2 5

40 14 15 
['binary search', 'brute force', 'implementation', '*2100']