D. Top-Notch Insertionstime limit per test3 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputConsider the insertion sort algorithm used to sort an integer sequence [a_1, a_2, \ldots, a_n] of length n in non-decreasing order.For each i in order from 2 to n, do the following. If a_i \ge a_{i-1}, do nothing and move on to the next value of i. Otherwise, find the smallest j such that a_i < a_j, shift the elements on positions from j to i-1 by one position to the right, and write down the initial value of a_i to position j. In this case we'll say that we performed an insertion of an element from position i to position j.It can be noticed that after processing any i, the prefix of the sequence [a_1, a_2, \ldots, a_i] is sorted in non-decreasing order, therefore, the algorithm indeed sorts any sequence.For example, sorting [4, 5, 3, 1, 3] proceeds as follows:   i = 2: a_2 \ge a_1, do nothing;  i = 3: j = 1, insert from position 3 to position 1: [3, 4, 5, 1, 3];  i = 4: j = 1, insert from position 4 to position 1: [1, 3, 4, 5, 3];  i = 5: j = 3, insert from position 5 to position 3: [1, 3, 3, 4, 5]. You are given an integer n and a list of m integer pairs (x_i, y_i). We are interested in sequences such that if you sort them using the above algorithm, exactly m insertions will be performed: first from position x_1 to position y_1, then from position x_2 to position y_2, ..., finally, from position x_m to position y_m.How many sequences of length n consisting of (not necessarily distinct) integers between 1 and n, inclusive, satisfy the above condition? Print this number modulo 998\,244\,353.InputEach test contains multiple test cases. The first line contains the number of test cases t (1 \le t \le 10^5). Description of the test cases follows.The first line of each test case contains two integers n and m (2 \le n \le 2 \cdot 10^5; 0 \le m < n) — the length of the sequence and the number of insertions.The i-th of the following m lines contains two integers x_i and y_i (2 \le x_1 < x_2 < \ldots < x_m \le n; 1 \le y_i < x_i). These lines describe the sequence of insertions in chronological order.It is guaranteed that the sum of m over all test cases does not exceed 2 \cdot 10^5. Note that there is no constraint on the sum of n of the same kind.OutputFor each test case, print the number of sequences of length n consisting of integers from 1 to n such that sorting them with the described algorithm produces the given sequence of insertions, modulo 998\,244\,353.ExampleInput
3
3 0
3 2
2 1
3 1
5 3
3 1
4 1
5 3
Output
10
1
21
NoteIn the first test case, the algorithm performs no insertions — therefore, the initial sequence is already sorted in non-decreasing order. There are 10 such sequences: [1, 1, 1], [1, 1, 2], [1, 1, 3], [1, 2, 2], [1, 2, 3], [1, 3, 3], [2, 2, 2], [2, 2, 3], [2, 3, 3], [3, 3, 3].In the second test case, the only sequence satisfying the conditions is [3, 2, 1].In the third test case, [4, 5, 3, 1, 3] is one of the sought sequences.
3
3 0
3 2
2 1
3 1
5 3
3 1
4 1
5 3

10 1 21 
['combinatorics', 'data structures', '*2600']