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 lim = 5e5;
  int T, n, m, w, fc[500005], invF[500005];
  int rt, cntP;
  struct Point {
    int vl, w, sz, tg, ch[2];
  } pt[500005];
  int New(int vl, int w = rand()) {
    pt[++cntP] = (Point){vl, w, 1, 0, {0, 0}};
    return cntP;
  }
  void mdf(int p, int vl) {
    pt[p].vl += vl;
    pt[p].tg += vl;
  }
  void pu(int p) { pt[p].sz = pt[pt[p].ch[0]].sz + pt[pt[p].ch[1]].sz + 1; }
  void pd(int p) {
    if (pt[p].tg) {
      if (pt[p].ch[0]) mdf(pt[p].ch[0], pt[p].tg);
      if (pt[p].ch[1]) mdf(pt[p].ch[1], pt[p].tg);
      pt[p].tg = 0;
    }
  }
  void split(int p, int vl, int &pL, int &pR) {
    if (!p) {
      pL = pR = 0;
      return;
    }
    pd(p);
    if (pt[p].vl <= vl)
      pL = p, split(pt[p].ch[1], vl, pt[p].ch[1], pR);
    else
      pR = p, split(pt[p].ch[0], vl, pL, pt[p].ch[0]);
    pu(p);
  }
  int merge(int pL, int pR) {
    if (!pL || !pR) return pL | pR;
    if (pt[pL].w < pt[pR].w) {
      pd(pL);
      pt[pL].ch[1] = merge(pt[pL].ch[1], pR);
      pu(pL);
      return pL;
    } else {
      pd(pR);
      pt[pR].ch[0] = merge(pL, pt[pR].ch[0]);
      pu(pR);
      return pR;
    }
  }
  void ins(int x) {
    int p1 = 0, p2 = 0, t;
    if (x < 3)
      p2 = rt;
    else
      split(rt, x - 2, p1, p2);
    t = p2;
    while (pt[t].ch[0]) pd(t), t = pt[t].ch[0];
    if (t && pt[t].vl == x - 1) {
      mdf(p2, 1);
      rt = merge(p1, p2);
      return;
    }
    ++w;
    mdf(p2, 1);
    rt = merge(merge(p1, New(x)), p2);
  }
  int qPow(int x, int y) {
    int res = 1;
    for (; y; y /= 2, x = 1ll * x * x % 998244353)
      if (y & 1) res = 1ll * res * x % 998244353;
    return res;
  }
  int C(int x, int y) {
    return 1ll * fc[x] * invF[y] % 998244353 * invF[x - y] % 998244353;
  }
  void slv() {
    scanf("%d %d", &n, &m);
    w = rt = cntP = 0;
    for (int i = 1, x, y; i <= m; ++i) scanf("%d %d", &x, &y), ins(y);
    printf("%d\n", C(n * 2 - w - 1, n));
  }
  int main() {
    srand(time(0));
    fc[0] = invF[0] = 1;
    for (int i = 1; i <= lim; ++i) fc[i] = 1ll * fc[i - 1] * i % 998244353;
    invF[lim] = qPow(fc[lim], 998244353 - 2);
    for (int i = lim - 1; i; --i)
      invF[i] = 1ll * invF[i + 1] * (i + 1) % 998244353;
    scanf("%d", &T);
    while (T--) slv();
    return 0;
  }
  