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;
  template <typename T>
  inline bool chkmax(T &x, T y) {
    return (x < y) ? ((x = y), 1) : 0;
  }
  template <typename T>
  inline bool chkmin(T &x, T y) {
    return (x > y) ? ((x = y), 1) : 0;
  }
  const int NN = 2e5 + 10, RN = 2e5, Mod = 998244353;
  int T, N, M, x[NN], y[NN];
  int tr[NN];
  void add(int p, int v) {
    for (; p <= RN; p += ((p) & (-(p)))) tr[p] += v;
  }
  int query(int p) {
    int ret = 0;
    for (; p; p -= ((p) & (-(p)))) ret += tr[p];
    return ret;
  }
  int kth(int k) {
    int ret = 0;
    for (int i = 17; i >= 0; --i)
      if (ret + (1 << i) <= RN && k > tr[ret + (1 << i)]) {
        k -= tr[ret + (1 << i)];
        ret += (1 << i);
      }
    return ret + 1;
  }
  bool tag[NN];
  int ad(int x, int y) { return ((x + y) >= Mod) ? (x + y - Mod) : (x + y); }
  int dc(int x, int y) { return ((x - y) < 0) ? (x - y + Mod) : (x - y); }
  int ml(int x, int y) { return (long long)x * y % Mod; }
  int ksm(int x, int y) {
    int ret = 1;
    for (; y; y >>= 1, x = ml(x, x))
      if (y & 1) ret = ml(ret, x);
    return ret;
  }
  int fac[NN * 2], ifac[NN * 2];
  void prepare() {
    fac[0] = 1;
    for (int i = 1; i <= RN * 2; ++i) fac[i] = ml(fac[i - 1], i);
    ifac[RN * 2] = ksm(fac[RN * 2], Mod - 2);
    for (int i = RN * 2 - 1; i >= 0; --i) ifac[i] = ml(ifac[i + 1], i + 1);
  }
  int binom(int u, int d) {
    if (d < 0 || u < d) return 0;
    return ml(fac[u], ml(ifac[d], ifac[u - d]));
  }
  vector<int> clr1, clr2;
  int main() {
    scanf("%d", &T);
    for (int i = 1; i <= RN; ++i) add(i, 1);
    prepare();
    while (T--) {
      clr1.clear();
      clr2.clear();
      scanf("%d%d", &N, &M);
      for (int i = 1; i <= M; ++i) scanf("%d%d", &x[i], &y[i]);
      int cnt = N - 1;
      for (int i = M; i >= 1; --i) {
        int t1 = kth(y[i]), t2 = kth(y[i] + 1);
        add(t1, -1);
        clr1.push_back(t1);
        if (!tag[t2]) {
          tag[t2] = 1;
          --cnt;
          clr2.push_back(t2);
        }
      }
      printf("%d\n", binom(N + cnt, N));
      for (int i = 0; i < (int)clr1.size(); ++i) {
        add(clr1[i], 1);
      }
      for (int i = 0; i < (int)clr2.size(); ++i) {
        tag[clr2[i]] = 0;
      }
    }
    return 0;
  }
  