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 maxn = 400000, maxt = 200000, mod = 998244353;
  int test, n, m, x[222222], y[222222];
  int ls[222222], rs[222222], sz[222222], rd[222222], rt, l, r, rt1, rt2, rt3,
      cnt, jc[444444], injc[444444], key[222222], tag[222222];
  bool flg;
  int binpow(int a, int t) {
    int res = 1, p = a;
    for (int i = t; i; i >>= 1) {
      if (i & 1) res = 1ll * res * p % mod;
      p = 1ll * p * p % mod;
    }
    return res;
  }
  void Init() {
    jc[0] = 1;
    for (int i = 1; i <= maxn; i++) jc[i] = 1ll * jc[i - 1] * i % mod;
    injc[maxn] = binpow(jc[maxn], mod - 2);
    for (int i = maxn - 1; i >= 0; i--)
      injc[i] = 1ll * injc[i + 1] * (i + 1) % mod;
  }
  int C(int n, int k) { return 1ll * jc[n] * injc[k] % mod * injc[n - k] % mod; }
  void pushup(int x) { sz[x] = sz[ls[x]] + sz[rs[x]] + 1; }
  void push(int node, int x) {
    key[node] += x;
    tag[node] += x;
  }
  void pushdown(int node) {
    if (tag[node]) {
      if (ls[node]) push(ls[node], tag[node]);
      if (rs[node]) push(rs[node], tag[node]);
      tag[node] = 0;
    }
  }
  int merge(int x, int y) {
    if (!x || !y) return x ^ y;
    pushdown(x);
    pushdown(y);
    if (rd[x] <= rd[y]) {
      rs[x] = merge(rs[x], y);
      pushup(x);
      return x;
    } else {
      ls[y] = merge(x, ls[y]);
      pushup(y);
      return y;
    }
  }
  void split(int x, int &rt1, int &rt2, int y) {
    if (!x) {
      rt1 = rt2 = 0;
      return;
    }
    pushdown(x);
    if (key[x] == y) flg = 1;
    if (key[x] >= y) {
      rt2 = x;
      split(ls[x], rt1, ls[rt2], y);
      pushup(x);
    } else {
      rt1 = x;
      split(rs[x], rs[rt1], rt2, y);
      pushup(x);
    }
  }
  void Out(int x) {
    if (!x) return;
    pushdown(x);
    Out(ls[x]);
    printf("%d ", key[x]);
    Out(rs[x]);
  }
  int main() {
    scanf("%d", &test);
    Init();
    srand(time(0));
    for (int i = 1; i <= maxt; i++) rd[i] = i;
    random_shuffle(rd + 1, rd + maxt + 1);
    while (test--) {
      scanf("%d%d", &n, &m);
      for (int i = 1; i <= m; i++) {
        scanf("%d%d", &x[i], &y[i]);
      }
      rt = 0;
      cnt = 0;
      for (int i = 1; i <= m; i++) {
        if (y[i] == 1) {
          ++cnt;
          sz[cnt] = 1;
          key[cnt] = 1;
          tag[cnt] = 0;
          ls[cnt] = rs[cnt] = 0;
          push(rt, 1);
          rt = merge(cnt, rt);
        } else {
          flg = 0;
          split(rt, rt1, rt2, y[i] - 1);
          if (!flg) {
            ++cnt;
            sz[cnt] = 1;
            key[cnt] = y[i] - 1;
            tag[cnt] = 0;
            ls[cnt] = rs[cnt] = 0;
            rt3 = merge(cnt, rt2);
            push(rt3, 1);
            rt = merge(rt1, rt3);
          } else {
            push(rt2, 1);
            rt = merge(rt1, rt2);
          }
        }
      }
      printf("%d\n", C(n + n - 1 - cnt, n));
    }
    return 0;
  }
  