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;
  const int mod = 998244353;
  int n, m, jc[1000005] = {1}, ny[1000005] = {1}, ans = 0, X[1000005], Y[1000005];
  int C(int x, int y) {
    if (x < y || y < 0 || x < 0) return 0;
    return 1ll * jc[x] * ny[y] % mod * ny[x - y] % mod;
  }
  int Power(int x, int y) {
    int r = 1;
    while (y) {
      if (y & 1) r = 1ll * r * x % mod;
      x = 1ll * x * x % mod, y >>= 1;
    }
    return r;
  }
  int c[1000005][2], s[1000005], rnk[1000005], root = 0;
  unsigned int randseed = 19260817;
  int Rand() { return randseed = (randseed * 7 + 13) ^ (randseed / 13 - 7); }
  void Pushup(int x) { s[x] = s[c[x][0]] + 1 + s[c[x][1]]; }
  pair<int, int> Split(int x, int k) {
    if (!x) return {0, 0};
    if (s[c[x][0]] >= k) {
      pair<int, int> o = Split(c[x][0], k);
      return c[x][0] = o.second, Pushup(x), (pair<int, int>){o.first, x};
    } else {
      pair<int, int> o = Split(c[x][1], k - s[c[x][0]] - 1);
      return c[x][1] = o.first, Pushup(x), (pair<int, int>){x, o.second};
    }
  }
  int Merge(int x, int y) {
    if (!x || !y) return x + y;
    if (rnk[x] < rnk[y])
      return c[x][1] = Merge(c[x][1], y), Pushup(x), x;
    else
      return c[y][0] = Merge(x, c[y][0]), Pushup(y), y;
  }
  int Build(int l, int r) {
    if (l > r) return 0;
    if (l == r) return s[l] = 1, rnk[l] = Rand(), l;
    int mid = (l + r) / 2, p1 = Build(l, mid), p2 = Build(mid + 1, r);
    return Merge(p1, p2);
  }
  int Find(int x) {
    pair<int, int> o = Split(root, x - 1), oo = Split(o.second, 1);
    int ret = oo.first;
    return root = Merge(o.first, Merge(oo.first, oo.second)), ret;
  }
  void Shift(int x, int y) {
    pair<int, int> o = Split(root, x - 1), oo = Split(o.second, y - x),
                   ooo = Split(oo.second, 1);
    root = Merge(Merge(o.first, ooo.first), Merge(oo.first, ooo.second));
  }
  void Return(int x, int y) {
    pair<int, int> o = Split(root, x - 1), oo = Split(o.second, 1),
                   ooo = Split(oo.second, y - x);
    root = Merge(Merge(o.first, ooo.first), Merge(oo.first, ooo.second));
  }
  void Solve() {
    scanf("%d%d", &n, &m);
    int K = n - 1;
    for (int i = 1; i <= m; i++) {
      scanf("%d%d", &X[i], &Y[i]);
    }
    map<int, int> o;
    for (int i = 1, curmx = 0; i <= m; i++) {
      int x = X[i], y = Find(Y[i]);
      if (!o[y]) K--, o[y] = 1;
      Shift(Y[i], X[i]);
    }
    cout << C(n + K, n) << '\n';
    for (int i = m; i >= 1; i--) {
      Return(Y[i], X[i]);
    }
  }
  int main() {
    for (int i = 1; i <= 400000; i++) jc[i] = 1ll * jc[i - 1] * i % mod;
    ny[400000] = Power(jc[400000], mod - 2);
    for (int i = 399999; i; i--) ny[i] = 1ll * ny[i + 1] * (i + 1) % mod;
    root = Build(1, 200000);
    int t;
    scanf("%d", &t);
    while (t--) Solve();
    return 0;
  }
  