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;
  using cd = complex<double>;
  mt19937 rnd(chrono::system_clock::now().time_since_epoch().count());
  const long long mod = 998244353;
  const long long N = 4e5;
  long long p1[N + 5], p2[N + 5], tree[200005], a[200005], c[200005], n;
  long long C(long long a, long long b) {
    return (p1[a] % mod * p2[b] % mod * p2[a - b] % mod) % mod;
  }
  long long qpow(long long a, long long b) {
    long long res = 1;
    while (b) {
      if (b & 1) res = res * a % mod;
      a = a * a % mod;
      b /= 2;
    }
    return res % mod;
  }
  void add(long long x, long long y) {
    while (x <= 200001) {
      tree[x] += y;
      x += x & (-x);
    }
  }
  long long query(long long x) {
    long long res = 0;
    while (x) {
      res += tree[x];
      x -= x & (-x);
    }
    return res;
  }
  long long get(long long x) {
    long long l = 1, r = n;
    while (r >= l) {
      long long mid = (l + r) / 2;
      if (query(mid) >= x)
        r = mid - 1;
      else
        l = mid + 1;
    }
    return l;
  }
  int main() {
    p1[0] = 1;
    for (long long i = 1; i <= N; i++) {
      p1[i] = p1[i - 1] * i % mod;
    }
    p2[N] = qpow(p1[N], mod - 2);
    for (long long i = N - 1; i >= 0; i--) {
      p2[i] = p2[i + 1] * (i + 1) % mod;
    }
    for (long long i = 1; i <= 200000; i++) add(i, 1);
    long long q;
    cin >> q;
    while (q--) {
      long long m, num = 0;
      cin >> n >> m;
      for (long long i = 1; i <= m; i++) {
        cin >> a[i] >> c[i];
      }
      vector<long long> g;
      for (long long i = m; i >= 1; i--) {
        long long v = get(c[i]);
        if (query(v + 1) - query(v) > 0) num++;
        add(v, -1);
        g.push_back(v);
      }
      cout << C(2 * n - 1 - num, n) % mod << endl;
      for (auto v : g) add(v, 1);
    }
  }
  