Instant Noodles

题意翻译

- 有 $t$ 组测试数据。 - 给出一张点数为 $2N$ 的二分图，其中右侧的第 $i$ 个点有点权为 $c_i$。 - 令 $S$ 表示左侧点的一个非空点集，设 $f(S)$ 表示右侧点中**至少与 $S$ 中一个点相连的点**的点权和。 - 请你求出，对于所有非空集合 $S$，$f(S)$ 的 $\gcd$ 为多少。 - $1 \leq t,\sum n,\sum m \leq 5\times 10^5$，$1 \leq c_i \leq 10^{12}$。

题目描述

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 $ (assume that GCD of empty set is $ 0 $ ). Wu is too tired after his training to solve this problem. Help him!

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1 \leq t \leq 500\,000 $ ) — the number of test cases in the given test set. Test case descriptions follow. The first line of each case description 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 respectively. The second line contains $ n $ integers $ c_i $ ( $ 1 \leq c_i \leq 10^{12} $ ). The $ i $ -th number describes the integer in the vertex $ i $ of the right half of the graph. Each of the following $ m $ lines contains a pair of integers $ u_i $ and $ v_i $ ( $ 1 \leq u_i, v_i \leq n $ ), describing an edge between the vertex $ u_i $ of the left half and the vertex $ v_i $ of the right half. It is guaranteed that the graph does not contain multiple edges. Test case descriptions are separated with empty lines. The total value of $ n $ across all test cases does not exceed $ 500\,000 $ , and the total value of $ m $ across all test cases does not exceed $ 500\,000 $ as well.

输出格式

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

输入输出样例

输入样例 #1

3
2 4
1 1
1 1
1 2
2 1
2 2

3 4
1 1 1
1 1
1 2
2 2
2 3

4 7
36 31 96 29
1 2
1 3
1 4
2 2
2 4
3 1
4 3

输出样例 #1

2
1
12

说明

The greatest common divisor of a set of integers is the largest integer $ g $ such that all elements of the set are divisible by $ g $ . In the first sample case vertices of the left half and vertices of the right half are pairwise connected, and $ f(S) $ for any non-empty subset is $ 2 $ , thus the greatest common divisor of these values if also equal to $ 2 $ . In the second sample case the subset $ \{1\} $ in the left half is connected to vertices $ \{1, 2\} $ of the right half, with the sum of numbers equal to $ 2 $ , and the subset $ \{1, 2\} $ in the left half is connected to vertices $ \{1, 2, 3\} $ of the right half, with the sum of numbers equal to $ 3 $ . Thus, $ f(\{1\}) = 2 $ , $ f(\{1, 2\}) = 3 $ , which means that the greatest common divisor of all values of $ f(S) $ is $ 1 $ .

题意翻译

- 有 $t$ 组测试数据。 - 给出一张点数为 $2N$ 的二分图，其中右侧的第 $i$ 个点有点权为 $c_i$。 - 令 $S$ 表示左侧点的一个非空点集，设 $f(S)$ 表示右侧点中**至少与 $S$ 中一个点相连的点**的点权和。 - 请你求出，对于所有非空集合 $S$，$f(S)$ 的 $\gcd$ 为多少。 - $1 \leq t,\sum n,\sum m \leq 5\times 10^5$，$1 \leq c_i \leq 10^{12}$。