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>
  struct Treap {
    Treap *l, *r;
    int w, k, lz;
    Treap() {}
    Treap(int _k) : l(0), r(0), w(1), k(_k), lz(0) {}
  } tp_node[262144];
  void pull(Treap *p) { p->w = 1 + (p->l ? p->l->w : 0) + (p->r ? p->r->w : 0); }
  void push(Treap *p) {
    if (p->l) p->l->lz += p->lz;
    if (p->r) p->r->lz += p->lz;
    p->k += p->lz, p->lz = 0;
  }
  Treap *merge(Treap *p, Treap *q) {
    if (!p || !q) return p ? p : q;
    return rand() % (p->w + q->w) < p->w
               ? (push(p), p->r = merge(p->r, q), pull(p), p)
               : (push(q), q->l = merge(p, q->l), pull(q), q);
  }
  std::pair<Treap *, Treap *> split(Treap *p, int k) {
    if (!p) return {0, 0};
    Treap *l, *m, *r;
    push(p);
    if (p->k < k)
      std::tie(m, r) = split(p->r, k), p->r = 0, pull(p), l = merge(p, m);
    else
      std::tie(l, m) = split(p->l, k), p->l = 0, pull(p), r = merge(m, p);
    return {l, r};
  }
  int inv(int a) {
    int k = 998244353 - 2;
    int r = 1;
    while (k) {
      if (k & 1) r = (long long int)r * a % 998244353;
      a = (long long int)a * a % 998244353;
      k >>= 1;
    }
    return r;
  }
  int fac[262144 * 2];
  int comb(int n, int m) {
    return (long long int)fac[n] * inv(fac[n - m]) % 998244353 * inv(fac[m]) %
           998244353;
  }
  int y[262144];
  int main() {
    fac[0] = 1;
    for (int i = 1; i < 262144 * 2; ++i)
      fac[i] = (long long int)fac[i - 1] * i % 998244353;
    int T;
    scanf("%d", &T);
    for (int tc = 1; tc <= T; ++tc) {
      int n, m;
      scanf("%d%d", &n, &m);
      Treap *rt = 0;
      for (int i = 0; i < m; ++i) scanf("%*d%d", &y[i]);
      for (int i = 0; i < m; ++i) {
        Treap *pl, *pr;
        std::tie(pl, rt) = split(rt, y[i] - 1);
        std::tie(rt, pr) = split(rt, y[i]);
        if (pr) pr->lz += 1;
        rt = new (tp_node + i) Treap(y[i]);
        rt = merge(pl, rt);
        rt = merge(rt, pr);
      }
      int k = rt ? rt->w : 0;
      k = n - 1 - k;
      0;
      int ans = comb(n + k, k);
      printf("%d\n", ans);
    }
    return 0;
  }
  