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>
  using namespace std;
  int n, m, x[200021], y[200021];
  long long fact[2 * 200021];
  void init() {
    fact[0] = 1;
    for (int i = (1); i <= (2 * 200021 - 1); i++)
      fact[i] = (fact[i - 1] * i) % 998244353;
  }
  long long qpow(long long a, int b) {
    long long ret = 1;
    for (; b; b >>= 1) {
      if (b & 1) (ret *= a) %= 998244353;
      (a *= a) %= 998244353;
    }
    return ret;
  }
  long long C(int n, int m) {
    return fact[n] * qpow(fact[m] * fact[n - m] % 998244353, 998244353 - 2) %
           998244353;
  }
  struct fhq_Treap {
    struct node {
      int dat, val, siz, aux;
      bool counts;
      int c[2];
    } t[200021];
    int root, cnt;
    void init() { root = cnt = 0; }
    int New(int val) {
      t[++cnt].val = val, t[cnt].siz = 1;
      t[cnt].dat = rand(), t[cnt].counts = true;
      t[cnt].c[0] = t[cnt].c[1] = t[cnt].aux = 0;
      return cnt;
    }
    void push_up(int x) { t[x].siz = t[t[x].c[0]].siz + t[t[x].c[1]].siz + 1; }
    void split(int x, int val, int &l, int &r, int lft) {
      if (x == 0) {
        l = r = 0;
        return;
      }
      int siz = t[t[x].c[0]].siz + lft;
      if (t[x].val - t[x].aux + siz <= val)
        l = x, split(t[x].c[1], val, t[x].c[1], r, siz + 1);
      else
        r = x, split(t[x].c[0], val, l, t[x].c[0], lft);
      push_up(x);
    }
    int merge(int l, int r) {
      if (l == 0 || r == 0) return l + r;
      if (t[l].dat > t[r].dat) {
        t[l].c[1] = merge(t[l].c[1], r), push_up(l);
        return l;
      } else {
        t[r].c[0] = merge(l, t[r].c[0]), push_up(r);
        return r;
      }
    }
    bool insert(int val) {
      int x, y, z;
      split(root, val - 2, x, y, 0);
      split(y, val - 1, y, z, t[x].siz);
      bool ret = !y || !t[y].counts;
      if (!ret) t[y].counts = false;
      int p = merge(x, y), q = New(val);
      t[q].aux = t[p].siz;
      root = merge(merge(p, q), z);
      return ret;
    }
  } Treap;
  int main() {
    srand(time(0));
    ios::sync_with_stdio(false);
    int T;
    cin >> T;
    init();
    while (T--) {
      cin >> n >> m;
      for (int i = (1); i <= (m); i++) cin >> x[i] >> y[i];
      int gap = n - m - 1;
      Treap.init();
      for (int i = (1); i <= (m); i++)
        if (!Treap.insert(y[i])) gap++;
      cout << C(n + gap, gap) << endl;
    }
    return 0;
  }
  