E. Count Secondstime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputCirno has a DAG (Directed Acyclic Graph) with n nodes and m edges. The graph has exactly one node that has no out edges. The i-th node has an integer a_i on it.Every second the following happens: Let S be the set of nodes x that have a_x > 0. For all x \in S, 1 is subtracted from a_x, and then for each node y, such that there is an edge from x to y, 1 is added to a_y.Find the first moment of time when all a_i become 0. Since the answer can be very large, output it modulo 998\,244\,353.InputThe first line contains a single integer t (1 \leq t \leq 1000) — the number of test cases. Description of test cases follows.The first line of each test case contains two integers n, m (1 \leq n, m \leq 1000) — the number of vertices and edges in the graph.The second line of each test case contains n integers a_1, a_2, \ldots, a_n (0 \leq a_i \leq 10^9) — the integer on vertices.Each line of the following m lines contains two integers x, y (1 \leq x, y \leq n), represent a directed edge from x to y. It is guaranteed that the graph is a DAG with no multi-edges, and there is exactly one node that has no out edges.It is guaranteed that both sum of n and sum of m over all test cases are less than or equal to 10\,000.OutputFor each test case, print an integer in a separate line — the first moment of time when all a_i become 0, modulo 998\,244\,353.ExampleInput
53 21 1 11 22 35 51 0 0 0 01 22 33 44 51 510 11998244353 0 0 0 998244353 0 0 0 0 01 22 33 44 55 66 77 88 99 101 37 95 61293 1145 9961 9961 19191 22 33 45 41 42 46 910 10 10 10 10 101 21 32 34 36 33 56 56 16 2Output
3
5
4
28010
110
NoteIn the first test case: At time 0, the values of the nodes are [1, 1, 1].  At time 1, the values of the nodes are [0, 1, 1].  At time 2, the values of the nodes are [0, 0, 1].  At time 3, the values of the nodes are [0, 0, 0].So the answer is 3. In the second test case:  At time 0, the values of the nodes are [1, 0, 0, 0, 0].  At time 1, the values of the nodes are [0, 1, 0, 0, 1].  At time 2, the values of the nodes are [0, 0, 1, 0, 0].  At time 3, the values of the nodes are [0, 0, 0, 1, 0].  At time 4, the values of the nodes are [0, 0, 0, 0, 1].  At time 5, the values of the nodes are [0, 0, 0, 0, 0].  So the answer is 5.In the third test case:The first moment of time when all a_i become 0 is 6\cdot 998244353 + 4.
53 21 1 11 22 35 51 0 0 0 01 22 33 44 51 510 11998244353 0 0 0 998244353 0 0 0 0 01 22 33 44 55 66 77 88 99 101 37 95 61293 1145 9961 9961 19191 22 33 45 41 42 46 910 10 10 10 10 101 21 32 34 36 33 56 56 16 2
3 5 4 28010 110 
['brute force', 'constructive algorithms', 'dp', 'graphs', 'implementation', 'math', '*2200']