description: Consider the insertion sort algorithm used to sort an integer sequence [a_1, a_2, …, a_n] of length n in non-decreasing order.
  
  For each i in order from 2 to n, do the following. If a_i ≥ 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, …, 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 ≥ 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.
  
  Input
  
  Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^5). Description of the test cases follows.
  
  The first line of each test case contains two integers n and m (2 ≤ n ≤ 2 ⋅ 10^5; 0 ≤ 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 ≤ x_1 < x_2 < … < x_m ≤ n; 1 ≤ 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 ⋅ 10^5. Note that there is no constraint on the sum of n of the same kind.
  
  Output
  
  For 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.
  
  Example
  
  Input
  
  
  3
  3 0
  3 2
  2 1
  3 1
  5 3
  3 1
  4 1
  5 3
  
  
  Output
  
  
  10
  1
  21
  
  Note
  
  In 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.
solution: #include <bits/stdc++.h>
  const int M = 200005;
  const int N = 400000;
  const int mod = 998244353;
  int inv(int x, int k = mod - 2) {
    int r = 1;
    while (k) {
      if (k & 1) r = (long long)x * r % mod;
      x = (long long)x * x % mod;
      k >>= 1;
    }
    return r;
  }
  struct Binom {
    int fact[N + 1], infact[N + 1];
    Binom() {
      *fact = 1;
      for (int i = 1; i <= N; ++i) fact[i] = (long long)fact[i - 1] * i % mod;
      infact[N] = inv(fact[N]);
      for (int i = N; i; --i) infact[i - 1] = (long long)infact[i] * i % mod;
    }
    int operator()(const int a, const int b) const {
      return (a < b || b < 0)
                 ? 0
                 : ((long long)fact[a] * infact[b] % mod * infact[a - b] % mod);
    }
  } C;
  int n, m;
  int x[M], y[M];
  int fw[M];
  void add(int x, const int c) {
    for (; x < M; x += x & -x) fw[x] += c;
  }
  int qry(int x) {
    int res = 0;
    for (int i = 18; ~i; --i) {
      if ((res | 1 << i) < M && fw[res | 1 << i] < x) {
        x -= fw[res |= 1 << i];
      }
    }
    return res + 1;
  }
  int work() {
    static int b[M];
    static bool st[M];
    int res = 0;
    for (int i = m; i; --i) {
      int t = qry(y[i]);
      b[i] = t;
      if (!st[t + 1]) ++res;
      st[t] = true;
      add(t, -1);
    }
    for (int i = 1; i <= m; ++i) {
      st[b[i]] = false;
      add(b[i], 1);
    }
    return res;
  }
  int main() {
    int task;
    for (int i = 1; i < M; ++i) add(i, 1);
    for (scanf("%d", &task); task--;) {
      scanf("%d%d", &n, &m);
      for (int i = 1; i <= m; ++i) {
        scanf("%d%d", x + i, y + i);
      }
      printf("%d\n", C(2 * n - work() - 1, n));
    }
    return 0;
  }
  