Instant Noodles

Wu got hungry after an intense training session, and came to a nearby store to buy his favourite instant noodles. After Wu paid for his purchase, the cashier gave him an interesting task.

You are given a bipartite graph with positive integers in all vertices of the right half. For a subset $S$ of vertices of the left half we define $N(S)$ as the set of all vertices of the right half adjacent to at least one vertex in $S$, and $f(S)$ as the sum of all numbers in vertices of $N(S)$. Find the greatest common divisor of $f(S)$ for all possible non-empty subsets $S$.

Wu is too tired after his training to solve this problem. Help him!

The first line contains a single integer $t$ ($1 \leq t \leq 500\,000$), the number of test cases. Test case descriptions follow.

The first line of each case contains two integers $n$ and $m$ ($1 \leq n, m \leq 500\,000$), the number of vertices in either half of the graph and the number of edges.

The second line contains $n$ integers $c_i$ ($1 \leq c_i \leq 10^{12}$). The $i$-th number is the integer written on vertex $i$ of the right half.

Each of the following $m$ lines contains a pair of integers $u_i$ and $v_i$ ($1 \leq u_i, v_i \leq n$), meaning there is an edge between vertex $u_i$ of the left half and vertex $v_i$ of the right half. No multiple edges are given.

Test case descriptions are separated with empty lines. The total of $n$ across all test cases does not exceed 500,000, and the total of $m$ does not exceed 500,000 as well.

For each test case, print a single integer, the required greatest common divisor.

The greatest common divisor of a set of integers is the largest integer $g$ such that every element of the set is divisible by $g$.

In the first sample case, every left vertex is connected to every right vertex, so $f(S) = 2$ for every non-empty subset $S$, and the greatest common divisor is 2.

In the second sample case, the subset $\{1\}$ of the left half is connected to the right vertices $\{1, 2\}$, and their sum is 2. The subset $\{1, 2\}$ is connected to the right vertices $\{1, 2, 3\}$, with sum 3. So $f(\{1\}) = 2$ and $f(\{1, 2\}) = 3$, and the greatest common divisor of all values of $f(S)$ is 1.